{"id":1200,"date":"2018-12-11T13:23:28","date_gmt":"2018-12-11T18:23:28","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/chapter\/use-a-problem-solving-strategy-2\/"},"modified":"2018-12-11T13:23:28","modified_gmt":"2018-12-11T18:23:28","slug":"use-a-problem-solving-strategy-2","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/chapter\/use-a-problem-solving-strategy-2\/","title":{"raw":"Use a Problem Solving Strategy","rendered":"Use a Problem Solving Strategy"},"content":{"raw":"\n[latexpage]<div class=\"textbox textbox--learning-objectives\"><h3 itemprop=\"educationalUse\">Learning Objectives<\/h3>By the end of this section, you will be able to: <ul><li>Use a problem solving strategy for word problems<\/li><li>Solve number word problems<\/li><li>Solve percent applications<\/li><li>Solve simple interest applications<\/li><\/ul><\/div><div data-type=\"note\" id=\"fs-id1167836288591\" class=\"be-prepared\"><p id=\"fs-id1167836356925\">Before you get started, take this readiness quiz.<\/p><ol id=\"fs-id1167836543609\" type=\"1\"><li>Translate \u201csix less than twice <em data-effect=\"italics\">x<\/em>\u201d into an algebraic expression.<div data-type=\"newline\"><br><\/div> If you missed this problem, review <a href=\"\/contents\/d3697553-3900-453f-8c08-8f74d55711ba#fs-id1167836513192\" class=\"autogenerated-content\">(Figure)<\/a>.<\/li><li>Convert 4.5% to a decimal.<div data-type=\"newline\"><br><\/div> If you missed this problem, review <a href=\"\/contents\/99b2296a-9957-4380-aff4-248abadc862b#fs-id1167829721053\" class=\"autogenerated-content\">(Figure)<\/a>.<\/li><li>Convert 0.6 to a percent.<div data-type=\"newline\"><br><\/div> If you missed this problem, review <a href=\"\/contents\/99b2296a-9957-4380-aff4-248abadc862b#fs-id1167829721053\" class=\"autogenerated-content\">(Figure)<\/a>.<\/li><\/ol><\/div><p id=\"fs-id1167833223914\">Have you ever had any negative experiences in the past with word problems? When we feel we have no control, and continue repeating negative thoughts, we set up barriers to success. Realize that your negative experiences with word problems are in your past. To move forward you need to calm your fears and change your negative feelings.<\/p><p id=\"fs-id1167829599677\">Start with a fresh slate and begin to think positive thoughts. Repeating some of the following statements may be helpful to turn your thoughts positive. Thinking positive thoughts is a first step towards success.<\/p><p id=\"fs-id1166401559623\">\u2003\u2003I think I can! I think I can!<\/p><p id=\"fs-id1167836544756\">\u2003\u2003While word problems were hard in the past, I think I can try them now.<\/p><p id=\"fs-id1167836551851\">\u2003\u2003I am better prepared now\u2014I think I will begin to understand word problems.<\/p><p id=\"fs-id1167836379098\">\u2003\u2003I am able to solve equations because I practiced many problems and I got help when I needed it\u2014I can try that<\/p><div data-type=\"newline\"><br><\/div>\u2003\u2003with word problems.<p id=\"fs-id1167833055883\">\u2003\u2003It may take time, but I can begin to solve word problems.<\/p><p id=\"fs-id1167833224302\">You are now well prepared and you are ready to succeed. If you take control and believe you can be successful, you will be able to master word problems.<\/p><div class=\"bc-section section\" data-depth=\"1\" id=\"fs-id1167836607409\"><h3 data-type=\"title\">Use a Problem Solving Strategy for Word Problems<\/h3><p id=\"fs-id1167836688094\">Now that we can solve equations, we are ready to apply our new skills to word problems. We will develop a strategy we can use to solve any word problem successfully.<\/p><div data-type=\"example\" id=\"fs-id1167833053847\" class=\"textbox textbox--examples\"><div data-type=\"exercise\" id=\"fs-id1167836528531\"><div data-type=\"problem\" id=\"fs-id1167836293464\"><p id=\"fs-id1167836387267\">Normal yearly snowfall at the local ski resort is 12 inches more than twice the amount it received last season. The normal yearly snowfall is 62 inches. What was the snowfall last season at the ski resort?<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167833097195\"><table id=\"fs-id1167829809695\" class=\"unnumbered unstyled can-break\" summary=\"Step 1 is to read the problem. Step 2 is to identify what you are looking for. What was the snowfall last season? Step 3 is to name what we are looking for and choose a variable to represent it. Let s be equal to the snowfall last season. Step 4 is to translate. Restate the problem in one sentence with all the important information. The normal snowfall is 62, was is the equals sign, and twelve more than twice the amount last year is 2 s plus 12. The equation is 62 is equal to 2 s plus 12. Step 5 is to solve the equation. Subtract 12 from each side. The result is 62 minus 12 is equal to 2 s plus 12 minus 12. Simplify. The result is 50 is equal to 2 s. Divide each side by 2. The result is 50 divided by 2 is equal to 2 s divided by 2. Simplify. The result is 25 is equal to s. Step 6 is to check the solution. First is our answer reasonable? Yes, having 25 inches of snow seems OK. The problem says the normal snowfall is twelve inches more than twice the number of last season. Twice 25 is 50 and 12 more than that is 62. Step 7 is to answer the question. The snowfall last season was 25 inches.\" data-label=\"\"><tbody><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 1. Read<\/strong> the problem.<\/td><td><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 2. Identify<\/strong> what you are looking for.<\/td><td data-valign=\"top\" data-align=\"left\">What was the snowfall last season?<\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 3. Name<\/strong> what we are looking for and<div data-type=\"newline\"><br><\/div>choose a variable to represent it.<\/td><td data-valign=\"top\" data-align=\"left\">Let \\(s=\\) the snowfall last season.<\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 4. Translate.<\/strong><div data-type=\"newline\"><br><\/div>Restate the problem in one sentence with all the important information.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836700619\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_001a_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Translate into an equation.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836355755\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_001b_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 5. Solve<\/strong> the equation.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836448458\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_001c_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Subtract 12 from each side.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836448581\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_001d_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Simplify.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167833057954\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_001e_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Divide each side by two.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836694120\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_001f_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Simplify.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836596014\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_001g_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td colspan=\"2\" data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 6. Check:<\/strong> First, is our answer reasonable?<div data-type=\"newline\"><br><\/div>Yes, having 25 inches of snow seems OK.<div data-type=\"newline\"><br><\/div>The problem says the normal snowfall is twelve<div data-type=\"newline\"><br><\/div>inches more than twice the number of last season.<div data-type=\"newline\"><br><\/div>Twice 25 is 50 and 12 more than that is 62.<\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 7. Answer<\/strong> the question.<\/td><td data-valign=\"top\" data-align=\"left\">The snowfall last season was 25 inches.<\/td><\/tr><\/tbody><\/table><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167836292778\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167829742302\"><div data-type=\"problem\" id=\"fs-id1167829598115\"><p id=\"fs-id1167829719164\">Guillermo bought textbooks and notebooks at the bookstore. The number of textbooks was three more than twice the number of notebooks. He bought seven textbooks. How many notebooks did he buy?<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836326498\"><p id=\"fs-id1167833361713\">He bought two notebooks.<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167829756413\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167826170319\"><div data-type=\"problem\" id=\"fs-id1167833055336\"><p id=\"fs-id1167836492140\">Gerry worked Sudoku puzzles and crossword puzzles this week. The number of Sudoku puzzles he completed is eight more than twice the number of crossword puzzles. He completed 22 Sudoku puzzles. How many crossword puzzles did he do?<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836701489\"><p id=\"fs-id1167836288517\">He did seven crosswords puzzles.<\/p><\/div><\/div><\/div><p id=\"fs-id1167836551928\">We summarize an effective strategy for problem solving.<\/p><div data-type=\"note\" id=\"fs-id1167836407180\" class=\"howto\"><div data-type=\"title\">Use a Problem Solving Strategy for word problems.<\/div><ol id=\"fs-id1167836287137\" type=\"1\" class=\"stepwise\"><li><strong data-effect=\"bold\">Read<\/strong> the problem. Make sure all the words and ideas are understood.<\/li><li><strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/li><li><strong data-effect=\"bold\">Name<\/strong> what you are looking for. Choose a variable to represent that quantity.<\/li><li><strong data-effect=\"bold\">Translate<\/strong> into an equation. It may be helpful to restate the problem in one sentence with all the important information. Then, translate the English sentence into an algebra equation.<\/li><li><strong data-effect=\"bold\">Solve<\/strong> the equation using proper algebra techniques.<\/li><li><strong data-effect=\"bold\">Check<\/strong> the answer in the problem to make sure it makes sense.<\/li><li><strong data-effect=\"bold\">Answer<\/strong> the question with a complete sentence.<\/li><\/ol><\/div><\/div><div class=\"bc-section section\" data-depth=\"1\"><h3 data-type=\"title\">Solve Number Word Problems<\/h3><p id=\"fs-id1167836722637\">We will now apply the problem solving strategy to \u201cnumber word problems.\u201d Number word problems give some clues about one or more numbers and we use these clues to write an equation. Number word problems provide good practice for using the Problem Solving Strategy.<\/p><div data-type=\"example\" id=\"fs-id1167836525150\" class=\"textbox textbox--examples\"><div data-type=\"exercise\" id=\"fs-id1167833311015\"><div data-type=\"problem\" id=\"fs-id1167833050789\"><p id=\"fs-id1167836415272\">The sum of seven times a number and eight is thirty-six. Find the number.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836623937\"><table id=\"fs-id1167836612346\" class=\"unnumbered unstyled can-break\" summary=\"Did you notice that we left out some of the steps as we solved this equation? If you\u2019re not yet ready to leave out these steps, write down as many as you need. Step 1 is to read the problem. Step 2 is to identify what you are looking for. It is the number. Step 3 is name what you are look for and choose a variable to represent it. Let be equal to the number. Step 4 is to translate. Restate the problem as one sentence. The sum of seven times a number and 8 is 7 n plus 8, is the equals sign, and 36 is 36. Translate into an equation. The equation is 7 n plus 8 is equal to 36. Step 5 is to solve the equation. Subtract 7 from each side and simplify. The result is 7 n is equal to 28. Divide each side by 2 and simplify. The result is n is equal to 4. Step 6 is to check the solution. Is the sum of 7 times 4 plus 8 equal to 36? Is 28 plus 8 equal to 36? 36 is equal to 36. The solution checks. Step 7 is to answer the question. The number is 4.\" data-label=\"\"><tbody><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 1. Read<\/strong> the problem.<\/td><td><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 2. Identify<\/strong> what you are looking for.<\/td><td data-valign=\"top\" data-align=\"left\">the number<\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 3. Name<\/strong> what you are looking for and<div data-type=\"newline\"><br><\/div>choose a variable to represent it.<\/td><td data-valign=\"top\" data-align=\"left\">Let <em data-effect=\"italics\">n<\/em> = the number.<\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 4. Translate:<\/strong><div data-type=\"newline\"><br><\/div>Restate the problem as one sentence.<div data-type=\"newline\"><br><\/div>Translate into an equation.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836691731\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_002a_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167836539753\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_002b_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 5. Solve<\/strong> the equation.<div data-type=\"newline\"><br><\/div>Subtract eight from each side and simplify.<div data-type=\"newline\"><br><\/div>Divide each side by seven and simplify.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836391366\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_002c_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167832945886\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_002d_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167832999844\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_002e_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 6. Check.<\/strong><div data-type=\"newline\"><br><\/div>Is the sum of seven times four plus eight equal to 36?<div data-type=\"newline\"><br><\/div>\\(\\phantom{\\rule{2em}{0ex}}\\begin{array}{ccc}\\hfill 7\u00b74+8&amp; \\stackrel{?}{=}\\hfill &amp; 36\\hfill \\\\ \\hfill 28+8&amp; \\stackrel{?}{=}\\hfill &amp; 36\\hfill \\\\ \\hfill 36&amp; =\\hfill &amp; 36\u2713\\hfill \\end{array}\\)<\/td><td><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 7. Answer<\/strong> the question.<\/td><td data-valign=\"top\" data-align=\"left\">The number is 4.<\/td><\/tr><\/tbody><\/table><p id=\"fs-id1167829748097\">Did you notice that we left out some of the steps as we solved this equation? If you\u2019re not yet ready to leave out these steps, write down as many as you need.<\/p><\/div><\/div><\/div><div data-type=\"note\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167829693799\"><div data-type=\"problem\" id=\"fs-id1167833059816\"><p id=\"fs-id1167833369771\">The sum of four times a number and two is fourteen. Find the number.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167833021343\"><p id=\"fs-id1167836550075\">\\(3\\)<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167829906315\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167829580384\"><div data-type=\"problem\" id=\"fs-id1167829691197\"><p id=\"fs-id1167836520333\">The sum of three times a number and seven is twenty-five. Find the number.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836537101\"><p id=\"fs-id1167833057967\">\\(6\\)<\/p><\/div><\/div><\/div><p id=\"fs-id1167836327026\">Some number word problems ask us to find two or more numbers. It may be tempting to name them all with different variables, but so far, we have only solved equations with one variable. In order to avoid using more than one variable, we will define the numbers in terms of the same variable. Be sure to read the problem carefully to discover how all the numbers relate to each other.<\/p><div data-type=\"example\" id=\"fs-id1167829754000\" class=\"textbox textbox--examples\"><div data-type=\"exercise\" id=\"fs-id1167836620984\"><div data-type=\"problem\" id=\"fs-id1167836538090\"><p id=\"fs-id1167836449474\">The sum of two numbers is negative fifteen. One number is nine less than the other. Find the numbers.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836534850\"><table id=\"fs-id1167836312913\" class=\"unnumbered unstyled can-break\" summary=\"Step 1 is to read the problem. Step 2 is identify what you are looking for. It is two numbers. Step 3 is to name what you are looking for by choosing a variable to represent the first number. Let n be equal to the first number. One number is 9 less than the other. Let n minus 9 be equal to the second number. Step 4 is to translate. Write the sum of two numbers is negative 15. That is the first number plus the second number is negative 15. Translate it into an equation. The equation is n plus the quantity n minus 9 is equal to negative 15. Step 5 is to solve the equation. Combine like terms. The result is 2 n minus 9 is equal to negative 15. Add 9 to each side and simplify. The result is 2 n is equal to negative 6. Simplify. The result is n is equal negative 3, which is the first number. The expression, n minus 9, is the second number. Negative 3 minus 9 is negative 12. Step 6 is to check the solutions. Is negative 12 nine less than negative 3? Is negative 3 minus 9 equal to negative 12? Is negative 12 equal to negative 12? Is their sum negative 15? Is negative 3 plus negative 12 equal to negative 15? Negative 15 is equal to negative 15. The solutions check. Step 7 is to answer the question. The numbers are negative 3 and negative 12.\" data-label=\"\"><tbody><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 1. Read<\/strong> the problem.<\/td><td><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 2. Identify<\/strong> what you are looking for.<\/td><td data-valign=\"top\" data-align=\"left\">two numbers<\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 3. Name<\/strong> what you are looking for by<div data-type=\"newline\"><br><\/div>choosing a variable to represent the first<div data-type=\"newline\"><br><\/div>number.<div data-type=\"newline\"><br><\/div>\u201cOne number is nine less than the other.\u201d<\/td><td data-valign=\"top\" data-align=\"left\"><div data-type=\"newline\"><br><\/div>Let \\(n={1}^{\\text{st}}\\) number.<div data-type=\"newline\"><br><\/div><div data-type=\"newline\"><br><\/div>\\(n-9={2}^{\\text{nd}}\\) number<\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 4. Translate.<\/strong><div data-type=\"newline\"><br><\/div>Write as one sentence.<div data-type=\"newline\"><br><\/div>Translate into an equation.<\/td><td data-valign=\"top\" data-align=\"left\"><div data-type=\"newline\"><br><\/div>The sum of two numbers is negative fifteen.<div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167836287362\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_003a_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 5. Solve<\/strong> the equation.<div data-type=\"newline\"><br><\/div>Combine like terms.<div data-type=\"newline\"><br><\/div>Add nine to each side and simplify.<div data-type=\"newline\"><br><\/div>Simplify.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836415072\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_003b_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167829691498\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_003c_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167832999705\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_003d_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167836646293\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_003e_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><div data-type=\"newline\"><br><\/div><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167836732526\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_003f_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167833385719\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_003g_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><div data-type=\"newline\"><br><\/div><span data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_003h_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 6. Check.<\/strong><div data-type=\"newline\"><br><\/div>Is \\(-12\\) nine less than \\(-3?\\)<div data-type=\"newline\"><br><\/div>\\(\\phantom{\\rule{2em}{0ex}}\\begin{array}{ccc}\\hfill -3-9&amp; \\stackrel{?}{=}\\hfill &amp; -12\\hfill \\\\ \\hfill -12&amp; =\\hfill &amp; -12\u2713\\hfill \\end{array}\\)<div data-type=\"newline\"><br><\/div>Is their sum \\(-15?\\)<div data-type=\"newline\"><br><\/div>\\(\\phantom{\\rule{2em}{0ex}}\\begin{array}{ccc}\\hfill -3+\\left(-12\\right)&amp; \\stackrel{?}{=}\\hfill &amp; -15\\hfill \\\\ \\hfill -15&amp; =\\hfill &amp; -15\u2713\\hfill \\end{array}\\)<\/td><td><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 7. Answer<\/strong> the question.<\/td><td data-valign=\"top\" data-align=\"left\">The numbers are \\(-3\\) and \\(-12.\\)<\/td><\/tr><\/tbody><\/table><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167829832950\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167836363791\"><div data-type=\"problem\" id=\"fs-id1167836685299\"><p id=\"fs-id1167836288208\">The sum of two numbers is negative twenty-three. One number is seven less than the other. Find the numbers.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167829644871\"><p id=\"fs-id1167836391362\">\\(-15,-8\\)<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167833055971\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167830122597\"><div data-type=\"problem\" id=\"fs-id1167833058214\"><p id=\"fs-id1167833060864\">The sum of two numbers is negative eighteen. One number is forty more than the other. Find the numbers.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167829694885\"><p id=\"fs-id1167829627465\">\\(-29,11\\)<\/p><\/div><\/div><\/div><p id=\"fs-id1167833412513\">Some number problems involve <strong data-effect=\"bold\">consecutive integers<\/strong>. Consecutive integers are integers that immediately follow each other. Examples of <span data-type=\"term\">consecutive integers<\/span> are:<\/p><div data-type=\"equation\" id=\"fs-id1167836532368\" class=\"unnumbered\" data-label=\"\">\\(\\begin{array}{ccccccc}\\hfill 1,&amp; &amp; \\hfill 2,&amp; &amp; \\hfill 3,&amp; &amp; \\hfill 4\\\\ \\hfill -10,&amp; &amp; \\hfill -9,&amp; &amp; \\hfill -8,&amp; &amp; \\hfill -7\\\\ \\hfill 150,&amp; &amp; \\hfill 151,&amp; &amp; \\hfill 152,&amp; &amp; \\hfill 153\\end{array}\\)<\/div><p id=\"fs-id1167836798146\">Notice that each number is one more than the number preceding it. Therefore, if we define the first integer as <em data-effect=\"italics\">n<\/em>, the next consecutive integer is \\(n+1.\\) The one after that is one more than \\(n+1,\\) so it is \\(n+1+1,\\) which is \\(n+2.\\)<\/p><div data-type=\"equation\" id=\"fs-id1167836319415\" class=\"unnumbered\" data-label=\"\">\\(\\begin{array}{cccc}n\\hfill &amp; &amp; &amp; \\phantom{\\rule{4em}{0ex}}{1}^{\\text{st}}\\text{integer}\\hfill \\\\ n+1\\hfill &amp; &amp; &amp; \\phantom{\\rule{4em}{0ex}}{2}^{\\text{nd}}\\text{consecutive integer}\\hfill \\\\ n+2\\hfill &amp; &amp; &amp; \\phantom{\\rule{4em}{0ex}}{3}^{\\text{rd}}\\text{consecutive integer}\\phantom{\\rule{1.5em}{0ex}}\\text{etc.}\\hfill \\end{array}\\)<\/div><p id=\"fs-id1166401599563\">We will use this notation to represent consecutive integers in the next example.<\/p><div data-type=\"example\" id=\"fs-id1167836390345\" class=\"textbox textbox--examples\"><div data-type=\"exercise\" id=\"fs-id1167836408144\"><div data-type=\"problem\" id=\"fs-id1167836310249\"><p id=\"fs-id1167836313850\">Find three consecutive integers whose sum is \\(-54.\\)<\/p><\/div><div data-type=\"solution\"><table id=\"fs-id1167836327805\" class=\"unnumbered unstyled\" summary=\"Step 1 is to read the problem. Step 2 is to identify what we are looking for. They are three consecutive numbers. Step 3 is to name each of the three numbers. Let n be the first integer, n plus 1 the second consecutive integer, and n plus 2 the third consecutive integer. Step 4 is to translate. Restate as one sentence. The sum of the three integers is negative 54. Translate into an equation. The equation is n plus the quantity n plus 1 plus the quantity n plus 2 is equal to negative 54. Step 5 is to solve the equation. Combine like terms. The result is 3 n plus 3 is equal to negative 54. Subtract 3 from each side. The result is 3 n is equal to negative 57. Divide each side by 3. The result is n is equal to negative 19, which is the first integer. The expression n plus 1 is the second integer. Negative 19 plus 1 is negative 18. The expression n plus 2 is the third integer. Negative 19 plus 2 is negative 17. Step 6 is to check. Is negative 19 plus negative 18 plus negative 17 equal to 54? Negative 54 is equal to negative 54. The solutions check. Step 7 is to answer the question. The three consecutive integers are negative 17, negative 18, and negative 19.\" data-label=\"\"><tbody><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 1. Read<\/strong> the problem.<\/td><td><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 2. Identify<\/strong> what you are looking for.<\/td><td data-valign=\"top\" data-align=\"left\">three consecutive integers<\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 3. Name<\/strong> each of the three numbers<\/td><td data-valign=\"top\" data-align=\"left\">Let \\(n={1}^{\\text{st}}\\) integer.<div data-type=\"newline\"><br><\/div>\\(n+1={2}^{\\text{nd}}\\) consecutive integer<div data-type=\"newline\"><br><\/div>\\(n+2={3}^{\\text{rd}}\\) consecutive integer<\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 4. Translate.<\/strong><div data-type=\"newline\"><br><\/div>Restate as one sentence.<div data-type=\"newline\"><br><\/div>Translate into an equation.<\/td><td data-valign=\"top\" data-align=\"left\"><div data-type=\"newline\"><br><\/div>The sum of the three integers is \\(-54.\\)<div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167836283273\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_004a_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 5. Solve<\/strong> the equation.<div data-type=\"newline\"><br><\/div>Combine like terms.<div data-type=\"newline\"><br><\/div>Subtract three from each side.<div data-type=\"newline\"><br><\/div>Divide each side by three.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836511411\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_004b_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167833271911\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_004c_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><div data-type=\"newline\"><br><\/div><span data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_004d_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167836585175\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_004e_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><div data-type=\"newline\"><br><\/div><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167829590326\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_004f_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167836323283\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_004g_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167829721234\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_004h_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><div data-type=\"newline\"><br><\/div><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167829644849\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_004i_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167833019610\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_004j_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><div data-type=\"newline\"><br><\/div><span data-type=\"media\" id=\"fs-id1167833379868\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_004k_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 6. Check.<\/strong><div data-type=\"newline\"><br><\/div>\\(\\begin{array}{}\\\\ \\hfill -19+\\left(-18\\right)+\\left(-17\\right)&amp; =\\hfill &amp; -54\\hfill \\\\ \\hfill -54&amp; =\\hfill &amp; -54\u2713\\hfill \\end{array}\\)<\/td><td><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 7. Answer<\/strong> the question.<\/td><td data-valign=\"top\" data-align=\"left\">The three consecutive integers are<div data-type=\"newline\"><br><\/div>\\(-17,\\text{\u2212}\\text{18,}\\) and \\(-19.\\)<\/td><\/tr><\/tbody><\/table><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167836613008\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167833381624\"><div data-type=\"problem\" id=\"fs-id1167836418736\"><p id=\"fs-id1167836340296\">Find three consecutive integers whose sum is \\(-96.\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836613406\"><p id=\"fs-id1167836390229\">\\(-33,-32,-31\\)<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167836512861\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167829830056\"><div data-type=\"problem\" id=\"fs-id1167836552413\"><p id=\"fs-id1167836493421\">Find three consecutive integers whose sum is \\(-36.\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836729948\"><p id=\"fs-id1167836510061\">\\(-13,-12,-11\\)<\/p><\/div><\/div><\/div><p id=\"fs-id1167836481192\">Now that we have worked with consecutive integers, we will expand our work to include <span data-type=\"term\">consecutive even integers<\/span> and <span data-type=\"term\">consecutive odd integers<\/span>. Consecutive even integers are even integers that immediately follow one another. Examples of consecutive even integers are:<\/p><div data-type=\"equation\" id=\"fs-id1167836320620\" class=\"unnumbered\" data-label=\"\">\\(\\text{24, 26, 28}\\)<\/div><div data-type=\"equation\" id=\"fs-id1167836320621\" class=\"unnumbered\" data-label=\"\">\\(-12,-10,-8\\)<\/div><p id=\"fs-id1167829627793\">Notice each integer is two more than the number preceding it. If we call the first one <em data-effect=\"italics\">n<\/em>, then the next one is \\(n+2.\\) The one after that would be \\(n+2+2\\) or \\(n+4.\\)<\/p><div data-type=\"equation\" id=\"fs-id1167836392432\" class=\"unnumbered\" data-label=\"\">\\(\\begin{array}{cccc}n\\hfill &amp; &amp; &amp; \\phantom{\\rule{4em}{0ex}}{1}^{\\text{st}}\\text{even integer}\\hfill \\\\ n+2\\hfill &amp; &amp; &amp; \\phantom{\\rule{4em}{0ex}}{2}^{\\text{nd}}\\text{consecutive even integer}\\hfill \\\\ n+4\\hfill &amp; &amp; &amp; \\phantom{\\rule{4em}{0ex}}{3}^{\\text{rd}}\\text{consecutive even integer}\\phantom{\\rule{1.5em}{0ex}}\\text{etc.}\\hfill \\end{array}\\)<\/div><p id=\"fs-id1167836622525\">Consecutive odd integers are odd integers that immediately follow one another. Consider the consecutive odd integers 63, 65, and 67.<\/p><div data-type=\"equation\" id=\"fs-id1167836527062\" class=\"unnumbered\" data-label=\"\">\\(\\text{63, 65, 67}\\)<\/div><div data-type=\"equation\" id=\"fs-id1167836527063\" class=\"unnumbered\" data-label=\"\">\\(n,n+2,n+4\\)<\/div><div data-type=\"equation\" id=\"fs-id1167830012042\" class=\"unnumbered\" data-label=\"\">\\(\\begin{array}{cccc}n\\hfill &amp; &amp; &amp; \\phantom{\\rule{4em}{0ex}}{1}^{\\text{st}}\\text{odd integer}\\hfill \\\\ n+2\\hfill &amp; &amp; &amp; \\phantom{\\rule{4em}{0ex}}{2}^{\\text{nd}}\\text{consecutive odd integer}\\hfill \\\\ n+4\\hfill &amp; &amp; &amp; \\phantom{\\rule{4em}{0ex}}{3}^{\\text{rd}}\\text{consecutive odd integer}\\phantom{\\rule{1.5em}{0ex}}\\text{etc.}\\hfill \\end{array}\\)<\/div><p id=\"fs-id1167836434446\">Does it seem strange to have to add two (an even number) to get the next odd number? Do we get an odd number or an even number when we add 2 to 3? to 11? to 47?<\/p><p id=\"fs-id1167829906181\">Whether the problem asks for consecutive even numbers or odd numbers, you do not have to do anything different. The pattern is still the same\u2014to get to the next odd or the next even integer, add two.<\/p><div data-type=\"example\" id=\"fs-id1167836296968\" class=\"textbox textbox--examples\"><div data-type=\"exercise\" id=\"fs-id1167836285856\"><div data-type=\"problem\" id=\"fs-id1167829691674\"><p id=\"fs-id1167836299489\">Find three consecutive even integers whose sum is \\(120\\).<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836550296\"><p>\\(\\phantom{\\rule{4em}{0ex}}\\begin{array}{cc}\\mathbf{\\text{Step 1. Read}}\\phantom{\\rule{0.2em}{0ex}}\\text{the problem.}\\hfill &amp; \\\\ \\mathbf{\\text{Step 2. Identify}}\\phantom{\\rule{0.2em}{0ex}}\\text{what you are looking for.}\\hfill &amp; \\phantom{\\rule{2em}{0ex}}\\text{three consecutive even integers}\\hfill \\\\ \\mathbf{\\text{Step 3. Name.}}\\hfill &amp; \\phantom{\\rule{2em}{0ex}}\\text{Let}\\phantom{\\rule{0.2em}{0ex}}n=\\phantom{\\rule{0.2em}{0ex}}{1}^{\\text{st}}\\phantom{\\rule{0.2em}{0ex}}\\text{even integer.}\\hfill \\\\ &amp; \\phantom{\\rule{2em}{0ex}}n+2=\\phantom{\\rule{0.2em}{0ex}}{2}^{\\text{nd}}\\phantom{\\rule{0.2em}{0ex}}\\text{consecutive even integer}\\hfill \\\\ &amp; \\phantom{\\rule{2em}{0ex}}n+4=\\phantom{\\rule{0.2em}{0ex}}{3}^{\\text{rd}}\\phantom{\\rule{0.2em}{0ex}}\\text{consecutive even integer}\\hfill \\\\ \\mathbf{\\text{Step 4. Translate.}}\\hfill &amp; \\\\ \\text{Restate as one sentence.}\\hfill &amp; \\phantom{\\rule{2em}{0ex}}\\text{The sum of the three even integers is}\\phantom{\\rule{0.2em}{0ex}}120.\\hfill \\\\ \\text{Translate into an equation.}\\hfill &amp; \\phantom{\\rule{2em}{0ex}}n\\phantom{\\rule{0.2em}{0ex}}+\\phantom{\\rule{0.2em}{0ex}}n\\phantom{\\rule{0.2em}{0ex}}+\\phantom{\\rule{0.2em}{0ex}}2\\phantom{\\rule{0.2em}{0ex}}+\\phantom{\\rule{0.2em}{0ex}}n+4\\phantom{\\rule{0.2em}{0ex}}=120\\hfill \\\\ \\mathbf{\\text{Step 5. Solve}}\\phantom{\\rule{0.2em}{0ex}}\\text{the equation.}\\hfill &amp; \\phantom{\\rule{3.3em}{0ex}}n+n+2+n+4=120\\hfill \\\\ \\text{Combine like terms.}\\hfill &amp; \\phantom{\\rule{7.7em}{0ex}}3n+6=120\\hfill \\\\ \\text{Subtract 6 from each side.}\\hfill &amp; \\phantom{\\rule{9.5em}{0ex}}3n=114\\hfill \\\\ \\text{Divide each side by 3.}\\hfill &amp; \\phantom{\\rule{10em}{0ex}}n=38\\phantom{\\rule{1em}{0ex}}{1}^{\\text{st}}\\phantom{\\rule{0.2em}{0ex}}\\text{integer}\\hfill \\\\ \\\\ &amp; \\phantom{\\rule{11em}{0ex}}n+2\\phantom{\\rule{1em}{0ex}}{2}^{\\text{nd}}\\phantom{\\rule{0.2em}{0ex}}\\text{integer}\\hfill \\\\ &amp; \\phantom{\\rule{10.7em}{0ex}}38+2\\hfill \\\\ &amp; \\phantom{\\rule{11.5em}{0ex}}40\\hfill \\\\ \\\\ &amp; \\phantom{\\rule{11em}{0ex}}n+4\\phantom{\\rule{1em}{0ex}}{3}^{\\text{rd}}\\phantom{\\rule{0.2em}{0ex}}\\text{integer}\\hfill \\\\ &amp; \\phantom{\\rule{10.5em}{0ex}}38+4\\hfill \\\\ &amp; \\phantom{\\rule{12em}{0ex}}42\\hfill \\\\ \\mathbf{\\text{Step 6. Check.}}\\hfill &amp; \\\\ \\begin{array}{cc}\\hfill 38+40+42&amp; \\stackrel{?}{=}120\\hfill \\\\ \\hfill 120&amp; =120\\phantom{\\rule{0.2em}{0ex}}\u2713\\hfill \\end{array}\\hfill \\\\ \\mathbf{\\text{Step 7. Answer}}\\phantom{\\rule{0.2em}{0ex}}\\text{the question.}\\hfill &amp; \\phantom{\\rule{2em}{0ex}}\\text{The three consecutive integers are 38, 40, and 42.}\\hfill \\end{array}\\)<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167829741897\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167829741900\"><div data-type=\"problem\" id=\"fs-id1167836448166\"><p id=\"fs-id1167836448168\">Find three consecutive even integers whose sum is 102.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836318575\"><p id=\"fs-id1167836318578\">32, 34, 36<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167833379405\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167833379408\"><div data-type=\"problem\" id=\"fs-id1167833379410\"><p id=\"fs-id1167836387417\">Find three consecutive even integers whose sum is \\(-24.\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836320083\"><p id=\"fs-id1167836320085\">\\(-10,-8,-6\\)<\/p><\/div><\/div><\/div><p id=\"fs-id1167836606845\">When a number problem is in a real life context, we still use the same strategies that we used for the previous examples.<\/p><div data-type=\"example\" id=\"fs-id1167836606849\" class=\"textbox textbox--examples\"><div data-type=\"exercise\" id=\"fs-id1167829695606\"><div data-type=\"problem\" id=\"fs-id1167829695609\"><p id=\"fs-id1167829695611\">A married couple together earns ?110,000 a year. The wife earns ?16,000 less than twice what her husband earns. What does the husband earn?<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167829751395\"><p id=\"fs-id1167829714064\">\\(\\begin{array}{cccccc}\\mathbf{\\text{Step 1. Read}}\\phantom{\\rule{0.2em}{0ex}}\\text{the problem.}\\hfill &amp; &amp; &amp; &amp; &amp; \\\\ \\mathbf{\\text{Step 2. Identify}}\\phantom{\\rule{0.2em}{0ex}}\\text{what you are looking for.}\\hfill &amp; &amp; &amp; &amp; &amp; \\text{How much does the husband earn?}\\hfill \\\\ \\mathbf{\\text{Step 3. Name.}}\\hfill &amp; &amp; &amp; &amp; &amp; \\\\ \\text{Choose a variable to represent}\\hfill &amp; &amp; &amp; &amp; &amp; \\text{Let}\\phantom{\\rule{0.2em}{0ex}}h=\\text{the amount the husband earns.}\\hfill \\\\ \\text{the amount the husband earns.}\\hfill &amp; &amp; &amp; &amp; &amp; \\\\ \\text{The wife earns ?16,000 less than twice that.}\\hfill &amp; &amp; &amp; &amp; &amp; \\\\ \\mathbf{\\text{Step 4. Translate.}}\\hfill &amp; &amp; &amp; &amp; &amp; \\\\ \\begin{array}{c}\\text{Restate the problem in one sentence}\\hfill \\\\ \\text{with all the important information.}\\hfill \\\\ \\text{Translate into an equation.}\\hfill \\end{array}\\hfill &amp; &amp; &amp; &amp; &amp; \\begin{array}{c}2h-16,000=\\text{the amount the wife earns}\\hfill \\\\ \\text{Together the husband and wife earn ?110,000.}\\hfill \\end{array}\\hfill \\\\ &amp; &amp; &amp; &amp; &amp; \\begin{array}{ccc}\\hfill h+2h-16,000&amp; =\\hfill &amp; 110,000\\hfill \\end{array}\\hfill \\\\ \\begin{array}{c}\\mathbf{\\text{Step 5. Solve}}\\phantom{\\rule{0.2em}{0ex}}\\text{the equation.}\\hfill \\\\ \\text{Combine like terms.}\\hfill \\\\ \\text{Add 16,000 to both sides and simplify.}\\hfill \\\\ \\text{Divide each side by three.}\\hfill \\end{array}\\hfill &amp; &amp; &amp; &amp; &amp; \\begin{array}{ccc}\\hfill h+2h-16,000&amp; =\\hfill &amp; 110,000\\hfill \\\\ \\hfill 3h-16,000&amp; =\\hfill &amp; 110,000\\hfill \\\\ \\hfill 3h&amp; =\\hfill &amp; 126,000\\hfill \\\\ \\hfill h&amp; =\\hfill &amp; 42,000\\hfill \\end{array}\\hfill \\\\ &amp; &amp; &amp; &amp; &amp; \\hfill \\begin{array}{c}\\hfill \\text{?42,000 amount husband earns}\\hfill \\\\ \\\\ \\\\ \\hfill 2h-16,000\\phantom{\\rule{0.2em}{0ex}}\\text{amount wife earns}\\hfill \\\\ \\hfill 2\\left(42,000\\right)-16,000\\hfill \\\\ \\hfill 84,000-16,000\\hfill \\\\ \\hfill 68,000\\hfill \\end{array}\\hfill \\\\ \\mathbf{\\text{Step 6. Check:}}\\hfill &amp; &amp; &amp; &amp; &amp; \\\\ \\text{If the wife earns ?68,000 and the husband}\\hfill &amp; &amp; &amp; &amp; &amp; \\\\ \\text{earns ?42,000, is that ?110,000? Yes!}\\hfill &amp; &amp; &amp; &amp; &amp; \\\\ \\mathbf{\\text{Step 7. Answer}}\\phantom{\\rule{0.2em}{0ex}}\\text{the question.}\\hfill &amp; &amp; &amp; &amp; &amp; \\text{The husband earns ?42,000 a year.}\\hfill \\end{array}\\)<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167836579227\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167836579231\"><div data-type=\"problem\" id=\"fs-id1167836579233\"><p id=\"fs-id1167836352441\">According to the National Automobile Dealers Association, the average cost of a car in 2014 was ?28,400. This was ?1,600 less than six times the cost in 1975. What was the average cost of a car in 1975?<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836352447\"><p id=\"fs-id1167833019123\">The average cost was ?5,000.<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167833019129\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167836620867\"><div data-type=\"problem\" id=\"fs-id1167836620869\"><p id=\"fs-id1167836620872\">US Census data shows that the median price of new home in the U.S. in November 2014 was ?280,900. This was ?10,700 more than 14 times the price in November 1964. What was the median price of a new home in November 1964?<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836513568\"><p id=\"fs-id1167836513570\">The median price was ?19,300.<\/p><\/div><\/div><\/div><\/div><div class=\"bc-section section\" data-depth=\"1\" id=\"fs-id1167829683894\"><h3 data-type=\"title\">Solve Percent Applications<\/h3><p id=\"fs-id1167829788846\">There are several methods to solve percent equations. In algebra, it is easiest if we just translate English sentences into algebraic equations and then solve the equations. Be sure to change the given percent to a decimal before you use it in the equation.<\/p><div data-type=\"example\" id=\"fs-id1167829788852\" class=\"textbox textbox--examples\"><div data-type=\"exercise\" id=\"fs-id1167836300542\"><div data-type=\"problem\" id=\"fs-id1167836300544\"><p id=\"fs-id1167836300546\">Translate and solve:<\/p><p id=\"fs-id1167836300549\"><span class=\"token\">\u24d0<\/span> What number is 45% of 84?<\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span> 8.5% of what amount is ?4.76?<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d2<\/span> 168 is what percent of 112?<\/div><div data-type=\"solution\" id=\"fs-id1167836616212\"><p id=\"fs-id1167836616214\"><span class=\"token\">\u24d0<\/span><\/p><div data-type=\"newline\"><br><\/div><table id=\"fs-id1167833052126\" class=\"unnumbered unstyled\" summary=\"What number is 45% of 84? Translate into algebra. Let n be the number. Write is 45 percent of 84 as is equal to 0.45 times 84. Multiply. The result is n is equal 37.8. 37.8 is 45 percent of 84.\" data-label=\"\"><tbody><tr valign=\"top\"><td><\/td><td><\/td><td><\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167829807494\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_005a_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Translate into algebra. Let <em data-effect=\"italics\">n<\/em> <strong data-effect=\"bold\">=<\/strong> the number.<\/td><td><\/td><td><\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836492976\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_005b_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Multiply.<\/td><td><\/td><td><\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167829594470\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_005c_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td><\/td><td><\/td><td><\/td><td data-valign=\"top\" data-align=\"left\">37.8 is 45% of 84.<\/td><\/tr><\/tbody><\/table><p><\/p><div data-type=\"newline\"><br><\/div><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span><div data-type=\"newline\"><br><\/div><table id=\"fs-id1167829614288\" class=\"unnumbered unstyled\" summary=\"What number is 45% of 84? Translate into algebra. Let n be the number. Write is 45 percent of 84 as is equal to 0.45 times 84. Multiply. The result is n is equal 37.8. 37.8 is 45 percent of 84.\" data-label=\"\"><tbody><tr valign=\"top\"><td><\/td><td><\/td><td><\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836530002\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_006a_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Translate. Let <em data-effect=\"italics\">n<\/em> <strong data-effect=\"bold\">=<\/strong> the amount.<\/td><td><\/td><td><\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836545347\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_006b_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Multiply.<\/td><td><\/td><td><\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836375560\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_006c_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Divide both sides by 0.085 and simplify.<\/td><td><\/td><td><\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836699980\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_006d_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td><\/td><td><\/td><td><\/td><td data-valign=\"top\" data-align=\"left\">8.5% of ?56 is ?4.76<\/td><\/tr><\/tbody><\/table><p><\/p><div data-type=\"newline\"><br><\/div><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d2<\/span><div data-type=\"newline\"><br><\/div><table id=\"fs-id1167832925252\" class=\"unnumbered unstyled\" summary=\"168 is what percent of 112? We are asked to find the percent, so we must have our final result in percent form. Translate into algebra. Let p be equal to the percent. Write 168 is what percent of 112 as 168 is equal to p times 112. Multiply. The result is 168 is equal to 112 p. Divide both sides by 112 and simplify. The result is 1.5 is equal to p. Convert to a percent. The result is 150 percent is equal to p. 168 is 150 percent of 112.\" data-label=\"\"><tbody><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">We are asked to find percent, so we must<div data-type=\"newline\"><br><\/div>have our result in percent form.<\/td><td><\/td><td><\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836629052\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_007a_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Translate into algebra. Let <em data-effect=\"italics\">p<\/em> = the percent.<\/td><td><\/td><td><\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167833019737\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_007b_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Multiply.<\/td><td><\/td><td><\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167833369020\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_007c_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Divide both sides by 112 and simplify.<\/td><td><\/td><td><\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167829589453\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_007d_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Convert to percent.<\/td><td><\/td><td><\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836704270\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_007e_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td><\/td><td><\/td><td><\/td><td data-valign=\"top\" data-align=\"left\">168 is 150% of 112.<\/td><\/tr><\/tbody><\/table><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167829739356\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167829739361\"><div data-type=\"problem\" id=\"fs-id1167829739363\"><p id=\"fs-id1167833350221\">Translate and solve: <span class=\"token\">\u24d0<\/span> What number is 45% of 80? <span class=\"token\">\u24d1<\/span> 7.5% of what amount is ?1.95? <span class=\"token\">\u24d2<\/span> 110 is what percent of 88?<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836487171\"><p id=\"fs-id1167836487173\"><span class=\"token\">\u24d0<\/span> 36 <span class=\"token\">\u24d1<\/span> ?26 <span class=\"token\">\u24d2<\/span> \\(125%\\)<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167829719452\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167829719456\"><div data-type=\"problem\" id=\"fs-id1167829719458\"><p id=\"fs-id1167836375371\">Translate and solve: <span class=\"token\">\u24d0<\/span> What number is 55% of 60? <span class=\"token\">\u24d1<\/span> 8.5% of what amount is ?3.06? <span class=\"token\">\u24d0<\/span> 126 is what percent of 72?<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167832935652\"><p id=\"fs-id1167832935654\"><span class=\"token\">\u24d0<\/span> 33 <span class=\"token\">\u24d1<\/span> ?36 <span class=\"token\">\u24d0<\/span> \\(175%\\)<\/p><\/div><\/div><\/div><p id=\"fs-id1167836366381\">Now that we have a problem solving strategy to refer to, and have practiced solving basic percent equations, we are ready to solve percent applications. Be sure to ask yourself if your final answer makes sense\u2014since many of the applications we will solve involve everyday situations, you can rely on your own experience.<\/p><div data-type=\"example\" id=\"fs-id1167836699133\" class=\"textbox textbox--examples\"><div data-type=\"exercise\" id=\"fs-id1167829621049\"><div data-type=\"problem\" id=\"fs-id1167829621051\"><p id=\"fs-id1167829621053\">The label on Audrey\u2019s yogurt said that one serving provided 12 grams of protein, which is 24% of the recommended daily amount. What is the total recommended daily amount of protein?<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167829811256\"><table id=\"fs-id1167829621055\" class=\"unnumbered unstyled\" summary=\"What are you asked to find? What total amount of protein is recommended? Choose a variable to represent it. Let a be equal to the total amount of protein. Write a sentence that gives the information to find it. 12 grams is 24 percent of the total amount. So, 12 grams is 24 percent of a. Translate into an equation. 12 is equal to 0.24 times a. Solve. The result is 50 is equal to a. Check. Does this make sense? Yes, 24 percent is about one-fourth if the total and 12 is about one-fourth of 50. Write a complete sentence to answer the question. The amount of protein that is recommended is 50 grams.\" data-label=\"\"><tbody><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">What are you asked to find?<\/td><td data-valign=\"top\" data-align=\"left\">What total amount of protein is recommended?<\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Choose a variable to represent it.<\/td><td data-valign=\"top\" data-align=\"left\">Let \\(a=\\) total amount of protein.<\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Write a sentence that gives the<div data-type=\"newline\"><br><\/div>information to find it.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836627596\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_008a_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Translate into an equation.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836616307\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_008b_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Solve.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167833340112\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_008c_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Check: Does this make sense?<div data-type=\"newline\"><br><\/div>Yes, 24% is about \\(\\frac{1}{4}\\) of the total and<div data-type=\"newline\"><br><\/div>12 is about \\(\\frac{1}{4}\\) of 50.<\/td><td><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Write a complete sentence to answer the question.<\/td><td data-valign=\"top\" data-align=\"left\">The amount of protein that is recommended is 50 g.<\/td><\/tr><\/tbody><\/table><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167836543504\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167836543509\"><div data-type=\"problem\" id=\"fs-id1167836543511\"><p id=\"fs-id1167832940771\">One serving of wheat square cereal has 7 grams of fiber, which is 28% of the recommended daily amount. What is the total recommended daily amount of fiber?<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167832940776\"><p id=\"fs-id1167829687282\">25 grams<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167829687288\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167829720045\"><div data-type=\"problem\" id=\"fs-id1167829720047\"><p id=\"fs-id1167829720049\">One serving of rice cereal has 190 mg of sodium, which is 8% of the recommended daily amount. What is the total recommended daily amount of sodium?<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167829596261\"><p id=\"fs-id1167829596263\">2,375 mg<\/p><\/div><\/div><\/div><p id=\"fs-id1166401450383\">Remember to put the answer in the form requested. In the next example we are looking for the percent.<\/p><div data-type=\"example\" id=\"fs-id1167833023048\" class=\"textbox textbox--examples\"><div data-type=\"exercise\" id=\"fs-id1167833023050\"><div data-type=\"problem\" id=\"fs-id1167833023053\"><p id=\"fs-id1167836558499\">Veronica is planning to make muffins from a mix. The package says each muffin will be 240 calories and 60 calories will be from fat. What percent of the total calories is from fat?<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836558505\"><table id=\"fs-id1167829645113\" class=\"unnumbered unstyled\" summary=\"What are you asked to find? What percent of the total calories is fat? Choose a variable to represent it. Let p be equal to the percent of fat. Write a sentence that gives the information to find it. What percent of 240 is 60? The percent is p, of 240 is times 240, and is 60 is equal to 60. Translate the sentence into an equation. The equation is p times 240 is equal to 60. Multiply. The result is 240 p is equal to 60. Divided both sides by 240. The result is p is equal to 0.25. Put it in percent form. The result is p is equal to 25 percent. Check. Does this make sense? Yes, 25 percent is one-fourth. 60 is one-fourth of 240. So 25 percent makes sense. Write a complete sentence to answer the question. Of the total calories in each muffin, 25 percent is fat.\" data-label=\"\"><tbody><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">What are you asked to find?<\/td><td data-valign=\"top\" data-align=\"left\">What percent of the total calories is fat?<\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Choose a variable to represent it.<\/td><td data-valign=\"top\" data-align=\"left\">Let \\(p=\\) percent of fat.<\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Write a sentence that gives the<div data-type=\"newline\"><br><\/div>information to find it.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836492107\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_009a_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Translate the sentence into an equation.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167829595197\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_009b_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Multiply.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167829746767\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_009c_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Divide both sides by 240.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836626155\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_009d_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Put in percent form.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167829597278\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_009e_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Check: does this make sense?<div data-type=\"newline\"><br><\/div>Yes, \\(25%\\) is one-fourth; 60 is one-fourth<div data-type=\"newline\"><br><\/div>of 240. So, \\(25%\\) makes sense.<\/td><td><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Write a complete sentence to answer the question.<\/td><td data-valign=\"top\" data-align=\"left\">Of the total calories in each muffin, \\(25%\\) is fat.<\/td><\/tr><\/tbody><\/table><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167833329696\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167833329700\"><div data-type=\"problem\" id=\"fs-id1167833329703\"><p id=\"fs-id1167836606526\">Mitzi received some gourmet brownies as a gift. The wrapper said each 28% brownie was 480 calories, and had 240 calories of fat. What percent of the total calories in each brownie comes from fat? Round the answer to the nearest whole percent.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836606532\"><p id=\"fs-id1167836606534\">50%<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167833361796\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167836510879\"><div data-type=\"problem\" id=\"fs-id1167836510882\"><p id=\"fs-id1167836510884\">The mix Ricardo plans to use to make brownies says that each brownie will be 190 calories, and 76 calories are from fat. What percent of the total calories are from fat? Round the answer to the nearest whole percent.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167824720319\"><p id=\"fs-id1167824720321\">40%<\/p><\/div><\/div><\/div><p id=\"fs-id1167829614416\">It is often important in many fields\u2014business, sciences, pop culture\u2014to talk about how much an amount has increased or decreased over a certain period of time. This increase or decrease is generally expressed as a percent and called the <span data-type=\"term\">percent change<\/span>.<\/p><p id=\"fs-id1167836621821\">To find the percent change, first we find the amount of change, by finding the difference of the new amount and the original amount. Then we find what percent the amount of change is of the original amount.<\/p><div data-type=\"note\" class=\"howto\"><div data-type=\"title\">Find percent change.<\/div><ol id=\"fs-id1167833086566\" type=\"1\" class=\"stepwise\"><li>Find the amount of change.<div data-type=\"newline\"><br><\/div>\\(\\text{change}=\\text{new amount}-\\text{original amount}\\)<\/li><li>Find what percent the amount of change is of the original amount.<div data-type=\"newline\"><br><\/div>\\(\\text{change is what percent of the original amount?}\\)<\/li><\/ol><\/div><div data-type=\"example\" id=\"fs-id1167836598830\" class=\"textbox textbox--examples\"><div data-type=\"exercise\" id=\"fs-id1167836598832\"><div data-type=\"problem\" id=\"fs-id1167829743589\"><p id=\"fs-id1167829743591\">Recently, the California governor proposed raising community college fees from ?36 a unit to ?46 a unit. Find the percent change. (Round to the nearest tenth of a percent.)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167829743597\"><table id=\"fs-id1167836535293\" class=\"unnumbered unstyled\" summary=\"Find the amount of change. 46 minus 36 is equal to 10. Find the percent. Change is what percent of the original amount? Let p be equal to the percent. 10 is what percent of 36? Translate into an equation. 10 is equal to p times 36. Simplify. The result is 10 is equal to 36 p. Divide both sides 36. The result is 0.278 is approximately equal to p. Change to percent form. Round to the nearest tenth. 27.8 percent is approximately equal to p. Write a complete sentence to answer the question. The new fees are approximately a 27.8 percent increase over the old fees. Remember to round the division to the nearest thousandth in order to round the percent to the nearest tenth.\" data-label=\"\"><tbody><tr><td data-valign=\"top\" data-align=\"left\">Find the amount of change.<\/td><td data-valign=\"top\" data-align=\"left\">\\(46-36=10\\)<\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Find the percent.<\/td><td data-valign=\"top\" data-align=\"left\">Change is what percent of the original amount?<\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Let \\(p=\\) the percent.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167833224693\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_010a_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Translate to an equation.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836409496\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_010b_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Simplify.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836578846\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_010c_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Divide both sides by 36.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167824738972\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_010d_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Change to percent form; round to the<div data-type=\"newline\"><br><\/div>nearest tenth<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167833338974\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_010e_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Write a complete sentence to answer<div data-type=\"newline\"><br><\/div>the question.<\/td><td data-valign=\"top\" data-align=\"left\">The new fees are approximately a \\(27.8%\\) increase<div data-type=\"newline\"><br><\/div>over the old fees.<\/td><\/tr><tr valign=\"top\"><td colspan=\"2\" data-valign=\"top\" data-align=\"left\">Remember to round the division to the nearest thousandth in order to round the percent to the nearest tenth.<\/td><\/tr><\/tbody><\/table><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167833350522\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167836321413\"><div data-type=\"problem\" id=\"fs-id1167836321415\"><p id=\"fs-id1167836321418\">Find the percent change. (Round to the nearest tenth of a percent.) In 2011, the IRS increased the deductible mileage cost to 55.5 cents from 51 cents.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836738088\"><p id=\"fs-id1167836738091\">\\(8.8%\\)<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167829693674\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167836693062\"><div data-type=\"problem\" id=\"fs-id1167836693064\"><p id=\"fs-id1167836693066\">Find the percent change. (Round to the nearest tenth of a percent.) In 1995, the standard bus fare in Chicago was ?1.50. In 2008, the standard bus fare was 2.25.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167833024211\"><p id=\"fs-id1167833024214\">50%<\/p><\/div><\/div><\/div><p id=\"fs-id1167826172002\">Applications of discount and mark-up are very common in retail settings.<\/p><p id=\"fs-id1167826172005\">When you buy an item on sale, the original price has been discounted by some dollar amount. The <span data-type=\"term\">discount rate<\/span>, usually given as a percent, is used to determine the amount of the discount. To determine the <span data-type=\"term\">amount of discount<\/span>, we multiply the discount rate by the original price.<\/p><p id=\"fs-id1167836424195\">The price a retailer pays for an item is called the <span data-type=\"term\">original cost<\/span>. The retailer then adds a <span data-type=\"term\">mark-up<\/span> to the original cost to get the <span data-type=\"term\">list price<\/span>, the price he sells the item for. The mark-up is usually calculated as a percent of the original cost. To determine the amount of mark-up, multiply the mark-up rate by the original cost.<\/p><div data-type=\"note\" id=\"fs-id1167829590762\"><div data-type=\"title\">Discount<\/div><div data-type=\"equation\" id=\"fs-id1167829590767\" class=\"unnumbered\" data-label=\"\">\\(\\begin{array}{c}\\hfill \\text{amount of discount}=\\text{discount rate}\u00b7\\text{original price}\\hfill \\\\ \\hfill \\text{sale price}=\\text{original amount}\u2013\\text{discount price}\\hfill \\end{array}\\)<\/div><p id=\"fs-id1167833197288\">The sale price should always be less than the original price.<\/p><\/div><div data-type=\"note\"><div data-type=\"title\">Mark-up<\/div><div data-type=\"equation\" id=\"fs-id1167836375857\" class=\"unnumbered\" data-label=\"\">\\(\\begin{array}{c}\\hfill \\text{amount of mark-up}=\\text{mark-up rate}\u00b7\\text{original price}\\hfill \\\\ \\hfill \\text{list price}=\\text{original cost}\u2013\\text{mark-up}\\hfill \\end{array}\\)<\/div><p id=\"fs-id1167836692588\">The list price should always be more than the original cost.<\/p><\/div><div data-type=\"example\" id=\"fs-id1167836692592\" class=\"textbox textbox--examples\"><div data-type=\"exercise\" id=\"fs-id1167836692594\"><div data-type=\"problem\" id=\"fs-id1167829688721\"><p id=\"fs-id1167829688723\">Liam\u2019s art gallery bought a painting at an original cost of ?750. Liam marked the price up 40%. Find <span class=\"token\">\u24d0<\/span> the amount of mark-up and <span class=\"token\">\u24d1<\/span> the list price of the painting.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836730607\"><p id=\"fs-id1167836615159\"><span class=\"token\">\u24d0<\/span><\/p><div data-type=\"newline\"><br><\/div><div data-type=\"newline\"><br><\/div><table id=\"fs-id1167836615167\" class=\"unnumbered unstyled\" summary=\"Identify what you are asked to find, and choose a variable to represent it. What is the amount of mark-up? Let m be equal to the amount of mark up. Write a sentence that gives the information to find it. The mark-up is 40 percent of the 750 dollar original cost. Translate into an equation. The mark-up is m, is 40 percent is 0.40, of is multiplication, and the ?750 original cost is 750. The equation is m is equal to 0.40 times 750. Solve the equation. The result is m is equal to 300. Write a complete sentence. The mark-up on the painting was 300 dollars.\" data-label=\"\"><tbody><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Identify what you are asked to find, and<div data-type=\"newline\"><br><\/div>choose a variable to represent it.<\/td><td data-valign=\"top\" data-align=\"left\">What is the amount of mark-up?<div data-type=\"newline\"><br><\/div>Let \\(m=\\) the amount of mark-up.<\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Write a sentence that gives the<div data-type=\"newline\"><br><\/div>information to find it.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836731579\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_011a_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Translate into an equation.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167829850925\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_011b_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Solve the equation.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836620323\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_011c_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Write a complete sentence.<\/td><td data-valign=\"top\" data-align=\"left\">The mark-up on the painting was ?300.<\/td><\/tr><\/tbody><\/table><p><\/p><div data-type=\"newline\"><br><\/div><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span><div data-type=\"newline\"><br><\/div><table id=\"fs-id1167836694316\" class=\"unnumbered unstyled can-break\" summary=\"Identify what you are asked to find, and choose a variable to represent it. What is the list price? Let p be equal to the list price. Write a sentence that gives the information to find it. The list price is original cost plus the mark-up. The list price is p, is original cost is equal to 750, plus is the addition sign, the mark-up is 300. Translate into an equation. The result is p is equal to 750 plus 300. Solve the equation. The result is p is equal to 1050. Check. Is this list price more than the original cost? Is 1050 dollars more than 750 dollars? Yes. Write a complete sentence. The list price of the painting was 1050 dollars.\" data-label=\"\"><tbody><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Identify what you are asked to find, and<div data-type=\"newline\"><br><\/div>choose a variable to represent it.<\/td><td data-valign=\"top\" data-align=\"left\">What is the list price?<div data-type=\"newline\"><br><\/div>Let \\(p=\\) the list price.<\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Write a sentence that gives the<div data-type=\"newline\"><br><\/div>information to find it.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167833138766\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_012a_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Translate into an equation.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167829691960\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_012b_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Solve the equation.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167829748378\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_012c_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Check.<\/td><td data-valign=\"top\" data-align=\"left\">Is the list price more than the original cost?<div data-type=\"newline\"><br><\/div>Is ?1,050 more than ?750? Yes.<\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Write a complete sentence.<\/td><td data-valign=\"top\" data-align=\"left\">The list price of the painting was ?1,050.<\/td><\/tr><\/tbody><\/table><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167829712477\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167833024116\"><div data-type=\"problem\" id=\"fs-id1167833024118\"><p id=\"fs-id1167833024120\">Find <span class=\"token\">\u24d0<\/span> the amount of mark-up and <span class=\"token\">\u24d1<\/span> the list price: Jim\u2019s music store bought a guitar at original cost ?1,200. Jim marked the price up 50%.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836573666\"><p id=\"fs-id1167836573668\"><span class=\"token\">\u24d0<\/span> ?600 <span class=\"token\">\u24d1<\/span> ?1,800<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167836614575\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167836614579\"><div data-type=\"problem\" id=\"fs-id1167836614581\"><p id=\"fs-id1167836614583\">Find <span class=\"token\">\u24d0<\/span> the amount of mark-up and <span class=\"token\">\u24d1<\/span> the list price: The Auto Resale Store bought Pablo\u2019s Toyota for ?8,500. They marked the price up 35%.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167833059072\"><p id=\"fs-id1167833059074\"><span class=\"token\">\u24d0<\/span> ?2,975 <span class=\"token\">\u24d1<\/span> ?11,475<\/p><\/div><\/div><\/div><\/div><div class=\"bc-section section\" data-depth=\"1\" id=\"fs-id1167836507859\"><h3 data-type=\"title\">Solve Simple Interest Applications<\/h3><p id=\"fs-id1167836507865\">Interest is a part of our daily lives. From the interest earned on our savings to the interest we pay on a car loan or credit card debt, we all have some experience with interest in our lives.<\/p><p id=\"fs-id1167832927562\">The amount of money you initially deposit into a bank is called the <span data-type=\"term\">principal<\/span>, <em data-effect=\"italics\">P<\/em>, and the bank pays you <span data-type=\"term\">interest<\/span>, <em data-effect=\"italics\">I.<\/em> When you take out a loan, you pay interest on the amount you borrow, also called the principal.<\/p><p id=\"fs-id1167836707281\">In either case, the interest is computed as a certain percent of the principal, called the <span data-type=\"term\">rate of interest<\/span>, <em data-effect=\"italics\">r<\/em>. The rate of interest is usually expressed as a percent per year, and is calculated by using the decimal equivalent of the percent. The variable <em data-effect=\"italics\">t<\/em>, (for time) represents the number of years the money is saved or borrowed.<\/p><p id=\"fs-id1167836334286\">Interest is calculated as simple interest or compound interest. Here we will use simple interest.<\/p><div data-type=\"note\" id=\"fs-id1167829753593\"><div data-type=\"title\">Simple Interest<\/div><p id=\"fs-id1167829753599\">If an amount of money, <em data-effect=\"italics\">P<\/em>, called the principal, is invested or borrowed for a period of <em data-effect=\"italics\">t<\/em> years at an annual interest rate <em data-effect=\"italics\">r<\/em>, the amount of interest, <em data-effect=\"italics\">I<\/em>, earned or paid is<\/p><div data-type=\"equation\" id=\"fs-id1167836607407\" class=\"unnumbered\" data-label=\"\">\\(\\begin{array}{ccccccccccccc}&amp; &amp; &amp; &amp; &amp; &amp; &amp; &amp; &amp; &amp; \\hfill I&amp; =\\hfill &amp; \\text{interest}\\hfill \\\\ I=Prt\\hfill &amp; &amp; &amp; &amp; &amp; \\text{where}\\hfill &amp; &amp; &amp; &amp; &amp; \\hfill P&amp; =\\hfill &amp; \\text{principal}\\hfill \\\\ &amp; &amp; &amp; &amp; &amp; &amp; &amp; &amp; &amp; &amp; \\hfill r&amp; =\\hfill &amp; \\text{rate}\\hfill \\\\ &amp; &amp; &amp; &amp; &amp; &amp; &amp; &amp; &amp; &amp; \\hfill t&amp; =\\hfill &amp; \\text{time}\\hfill \\end{array}\\)<\/div><p id=\"fs-id1167829906930\">Interest earned or paid according to this formula is called <span data-type=\"term\">simple interest<\/span>.<\/p><\/div><p id=\"fs-id1167832951047\">The formula we use to calculate interest is \\(I=Prt.\\) To use the formula we substitute in the values for variables that are given, and then solve for the unknown variable. It may be helpful to organize the information in a chart.<\/p><div data-type=\"example\" id=\"fs-id1167836518198\" class=\"textbox textbox--examples\"><div data-type=\"exercise\" id=\"fs-id1167836518201\"><div data-type=\"problem\" id=\"fs-id1167836518203\"><p id=\"fs-id1167836518205\">Areli invested a principal of ?950 in her bank account that earned simple interest at an interest rate of 3%. How much interest did she earn in five years?<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836545229\"><p id=\"fs-id1167836545231\">\\(\\begin{array}{ccc}\\hfill I&amp; =\\hfill &amp; ?\\hfill \\\\ \\hfill P&amp; =\\hfill &amp; \\text{?}950\\hfill \\\\ \\hfill r&amp; =\\hfill &amp; 3%\\hfill \\\\ \\hfill t&amp; =\\hfill &amp; 5\\phantom{\\rule{0.2em}{0ex}}\\text{years}\\hfill \\end{array}\\)<\/p><p id=\"fs-id1167833137580\">\\(\\begin{array}{cccc}\\text{Identify what you are asked to find, and choose a}\\hfill &amp; &amp; &amp; \\phantom{\\rule{2em}{0ex}}\\text{What is the simple interest?}\\hfill \\\\ \\text{variable to represent it.}\\hfill &amp; &amp; &amp; \\phantom{\\rule{2em}{0ex}}\\text{Let}\\phantom{\\rule{0.2em}{0ex}}I=\\text{interest.}\\hfill \\\\ \\text{Write the formula.}\\hfill &amp; &amp; &amp; \\phantom{\\rule{3.5em}{0ex}}I=Prt\\hfill \\\\ \\text{Substitute in the given information.}\\hfill &amp; &amp; &amp; \\phantom{\\rule{3.5em}{0ex}}I=\\left(950\\right)\\left(0.03\\right)\\left(5\\right)\\hfill \\\\ \\text{Simplify.}\\hfill &amp; &amp; &amp; \\phantom{\\rule{3.5em}{0ex}}I=142.5\\hfill \\\\ \\text{Check.}\\hfill &amp; &amp; &amp; \\\\ \\text{Is ?142.50 a reasonable amount of interest on ?950?}\\hfill &amp; &amp; &amp; \\\\ \\text{Yes.}\\hfill &amp; \\\\ \\text{Write a complete sentence.}\\hfill &amp; &amp; &amp; \\phantom{\\rule{2em}{0ex}}\\text{The interest is ?142.50.}\\hfill \\end{array}\\)<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167833056117\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167829599078\"><div data-type=\"problem\" id=\"fs-id1167829599081\"><p id=\"fs-id1167829599083\">Nathaly deposited ?12,500 in her bank account where it will earn 4% simple interest. How much interest will Nathaly earn in five years?<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167829599088\"><p id=\"fs-id1167829893879\">He will earn ?2,500.<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167829893885\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167836526358\"><div data-type=\"problem\" id=\"fs-id1167836526361\"><p id=\"fs-id1167836526363\">Susana invested a principal of ?36,000 in her bank account that earned simple interest at an interest rate of \\(6.5%.\\) How much interest did she earn in three years?<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167829788278\"><p id=\"fs-id1167829859754\">She earned ?7,020.<\/p><\/div><\/div><\/div><p id=\"fs-id1167829859760\">There may be times when we know the amount of interest earned on a given principal over a certain length of time, but we do not know the rate.<\/p><div data-type=\"example\" id=\"fs-id1167829790848\" class=\"textbox textbox--examples\"><div data-type=\"exercise\" id=\"fs-id1167829790850\"><div data-type=\"problem\" id=\"fs-id1167829790852\"><p id=\"fs-id1167829790855\">Hang borrowed ?7,500 from her parents to pay her tuition. In five years, she paid them ?1,500 interest in addition to the ?7,500 she borrowed. What was the rate of simple interest?<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836407124\"><p id=\"fs-id1167836407127\">\\(\\begin{array}{ccc}\\hfill I&amp; =\\hfill &amp; \\text{?}1500\\hfill \\\\ \\hfill P&amp; =\\hfill &amp; \\text{?}7500\\hfill \\\\ \\hfill r&amp; =\\hfill &amp; ?\\hfill \\\\ \\hfill t&amp; =\\hfill &amp; 5\\phantom{\\rule{0.2em}{0ex}}\\text{years}\\hfill \\end{array}\\)<\/p><p id=\"fs-id1167829627509\">\\(\\begin{array}{cccc}\\text{Identify what you are asked to find, and choose}\\phantom{\\rule{2em}{0ex}}\\hfill &amp; &amp; &amp; \\text{What is the rate of simple interest?}\\hfill \\\\ \\begin{array}{c}\\text{a variable to represent it.}\\hfill \\\\ \\text{Write the formula.}\\hfill \\\\ \\text{Substitute in the given information.}\\hfill \\\\ \\text{Multiply.}\\hfill \\\\ \\text{Divide.}\\hfill \\\\ \\text{Change to percent form.}\\hfill \\end{array}\\hfill &amp; &amp; &amp; \\begin{array}{ccc}\\hfill \\text{Let}\\phantom{\\rule{0.2em}{0ex}}r&amp; =\\hfill &amp; \\text{rate of interest.}\\hfill \\\\ \\hfill I&amp; =\\hfill &amp; Prt\\hfill \\\\ \\hfill 1,500&amp; =\\hfill &amp; \\left(7,500\\right)r\\left(5\\right)\\hfill \\\\ \\hfill 1,500&amp; =\\hfill &amp; 37,500r\\hfill \\\\ \\hfill 0.04&amp; =\\hfill &amp; r\\hfill \\\\ \\hfill 4%&amp; =\\hfill &amp; r\\hfill \\end{array}\\hfill \\\\ \\text{Check.}\\hfill &amp; &amp; &amp; \\\\ \\begin{array}{ccc}\\hfill I&amp; =\\hfill &amp; Prt\\hfill \\\\ \\hfill 1,500&amp; \\stackrel{?}{=}\\hfill &amp; \\left(7,500\\right)\\left(0.04\\right)\\left(5\\right)\\hfill \\\\ \\hfill 1,500&amp; =\\hfill &amp; 1,500\u2713\\hfill \\end{array}\\hfill &amp; &amp; &amp; \\\\ \\text{Write a complete sentence.}\\hfill &amp; &amp; &amp; \\text{The rate of interest was 4%.}\\hfill &amp; &amp; &amp; \\end{array}\\)<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167836774787\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167836630614\"><div data-type=\"problem\" id=\"fs-id1167836630616\"><p id=\"fs-id1167836630618\">Jim lent his sister ?5,000 to help her buy a house. In three years, she paid him the ?5,000, plus ?900 interest. What was the rate of simple interest?<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836408266\"><p id=\"fs-id1167836408269\">The rate of simple interest was 6%.<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167836408275\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167836553008\"><div data-type=\"problem\" id=\"fs-id1167836553010\"><p id=\"fs-id1167836553012\">Loren lent his brother ?3,000 to help him buy a car. In four years, his brother paid him back the ?3,000 plus ?660 in interest. What was the rate of simple interest?<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167832961256\"><p id=\"fs-id1167832961259\">The rate of simple interest was 5.5%.<\/p><\/div><\/div><\/div><p id=\"fs-id1167832961265\">In the next example, we are asked to find the principal\u2014the amount borrowed.<\/p><div data-type=\"example\" id=\"fs-id1167836546286\" class=\"textbox textbox--examples\"><div data-type=\"exercise\" id=\"fs-id1167836546288\"><div data-type=\"problem\" id=\"fs-id1167836546290\"><p id=\"fs-id1167836546292\">Sean\u2019s new car loan statement said he would pay ?4,866,25 in interest from a simple interest rate of 8.5% over five years. How much did he borrow to buy his new car?<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167829879766\"><p id=\"fs-id1167829879769\">\\(\\begin{array}{ccc}\\hfill I&amp; =\\hfill &amp; 4,866.25\\hfill \\\\ \\hfill P&amp; =\\hfill &amp; ?\\hfill \\\\ \\hfill r&amp; =\\hfill &amp; 8.5%\\hfill \\\\ \\hfill t&amp; =\\hfill &amp; 5\\phantom{\\rule{0.2em}{0ex}}\\text{years}\\hfill \\end{array}\\)<\/p><p id=\"fs-id1167836558133\">\\(\\begin{array}{cccc}\\text{Identify what you are asked to find,}\\phantom{\\rule{2em}{0ex}}\\hfill &amp; &amp; &amp; \\text{What is the amount borrowed (the principal)?}\\hfill \\\\ \\begin{array}{c}\\text{and choose a variable to represent it.}\\hfill \\\\ \\text{Write the formula.}\\hfill \\\\ \\text{Substitute in the given information.}\\hfill \\\\ \\text{Multiply.}\\hfill \\\\ \\text{Divide.}\\hfill \\end{array}\\hfill &amp; &amp; &amp; \\begin{array}{ccc}\\hfill \\text{Let}\\phantom{\\rule{0.2em}{0ex}}P&amp; =\\hfill &amp; \\text{principal borrowed.}\\hfill \\\\ \\hfill I&amp; =\\hfill &amp; Prt\\hfill \\\\ \\hfill 4,866.25&amp; =\\hfill &amp; P\\left(0.085\\right)\\left(5\\right)\\hfill \\\\ \\hfill 4,866.25&amp; =\\hfill &amp; 0.425P\\hfill \\\\ \\hfill 11,450&amp; =\\hfill &amp; P\\hfill \\end{array}\\hfill \\\\ \\text{Check.}\\hfill &amp; &amp; &amp; \\\\ \\begin{array}{ccc}\\hfill I&amp; =\\hfill &amp; Prt\\hfill \\\\ \\hfill 4,866.25&amp; \\stackrel{?}{=}\\hfill &amp; \\left(11,450\\right)\\left(0.085\\right)\\left(5\\right)\\hfill \\\\ \\hfill 4,866.25&amp; =\\hfill &amp; 4,866.25\u2713\\hfill \\end{array}\\hfill &amp; &amp; &amp; \\\\ \\\\ \\\\ \\text{Write a complete sentence.}\\hfill &amp; &amp; &amp; \\text{The principal was ?11,450.}\\hfill \\end{array}\\)<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167836700880\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167836700884\"><div data-type=\"problem\" id=\"fs-id1167836518297\"><p>Eduardo noticed that his new car loan papers stated that with a 7.5% simple interest rate, he would pay ?6,596.25 in interest over five years. How much did he borrow to pay for his car?<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836518305\"><p id=\"fs-id1167836518307\">He paid ?17,590.<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167836729457\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167836729461\"><div data-type=\"problem\" id=\"fs-id1167836729463\"><p id=\"fs-id1167832989118\">In five years, Gloria\u2019s bank account earned ?2,400 interest at 5% simple interest. How much had she deposited in the account?<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167832989125\"><p id=\"fs-id1167832989127\">She deposited ?9,600.<\/p><\/div><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167829766743\" class=\"media-2\"><p id=\"fs-id1167829766746\">Access this online resource for additional instruction and practice with using a problem solving strategy.<\/p><ul id=\"fs-id1167833056662\" data-display=\"block\"><li><a href=\"https:\/\/openstax.org\/l\/37begalgwordpro\">Begining Arithmetic Problems<\/a><\/li><\/ul><\/div><div class=\"textbox\" data-depth=\"1\" id=\"fs-id1167836596031\"><h3 data-type=\"title\">Key Concepts<\/h3><ul id=\"fs-id1167836596038\" data-bullet-style=\"bullet\"><li><strong data-effect=\"bold\">How To Use a Problem Solving Strategy for Word Problems<\/strong><ol id=\"fs-id1167833224418\" type=\"1\" class=\"stepwise\"><li><strong data-effect=\"bold\">Read<\/strong> the problem. Make sure all the words and ideas are understood.<\/li><li><strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/li><li><strong data-effect=\"bold\">Name<\/strong> what you are looking for. Choose a variable to represent that quantity.<\/li><li><strong data-effect=\"bold\">Translate<\/strong> into an equation. It may be helpful to restate the problem in one sentence with all the important information. Then, translate the English sentence into an algebra equation.<\/li><li><strong data-effect=\"bold\">Solve<\/strong> the equation using proper algebra techniques.<div data-type=\"newline\"><br><\/div><p id=\"fs-id1167833051048\"><\/p><div data-type=\"newline\"><br><\/div><div data-type=\"newline\"><br><\/div><\/li><li><strong data-effect=\"bold\">Check<\/strong> the answer in the problem to make sure it makes sense.<\/li><li><strong data-effect=\"bold\">Answer<\/strong> the question with a complete sentence.<\/li><\/ol><\/li><li><strong data-effect=\"bold\">How To Find Percent Change<\/strong><ol type=\"1\" class=\"stepwise\"><li>Find the amount of change<div data-type=\"newline\"><br><\/div>\\(\\text{change}=\\text{new amount}-\\text{original amount}\\)<\/li><li>Find what percent the amount of change is of the original amount.<div data-type=\"newline\"><br><\/div>\\(\\text{change is what percent of the original amount?}\\)<\/li><\/ol><\/li><li><strong data-effect=\"bold\">Discount<\/strong><div data-type=\"newline\"><br><\/div>\\(\\begin{array}{ccc}\\hfill \\text{amount of discount}&amp; =\\hfill &amp; \\text{discount rate}\u00b7\\text{original price}\\hfill \\\\ \\\\ \\hfill \\text{sale price}&amp; =\\hfill &amp; \\text{original amount}-\\text{discount}\\hfill \\end{array}\\)<\/li><li><strong data-effect=\"bold\">Mark-up<\/strong><div data-type=\"newline\"><br><\/div>\\(\\begin{array}{ccc}\\hfill \\text{amount of mark-up}&amp; =\\hfill &amp; \\text{mark-up rate}\u00b7\\text{original cost}\\hfill \\\\ \\\\ \\hfill \\text{list price}&amp; =\\hfill &amp; \\text{original cost}\\phantom{\\rule{0.2em}{0ex}}+\\phantom{\\rule{0.2em}{0ex}}\\text{mark up}\\hfill \\end{array}\\)<\/li><li><strong data-effect=\"bold\">Simple Interest<\/strong><div data-type=\"newline\"><br><\/div> If an amount of money, <em data-effect=\"italics\">P<\/em>, called the principal, is invested or borrowed for a period of <em data-effect=\"italics\">t<\/em> years at an annual interest rate <em data-effect=\"italics\">r<\/em>, the amount of interest, <em data-effect=\"italics\">I<\/em>, earned or paid is:<div data-type=\"newline\"><br><\/div> <div data-type=\"equation\" id=\"fs-id1167835181891\" class=\"unnumbered\" data-label=\"\">\\(\\begin{array}{ccccc}&amp; &amp; I\\hfill &amp; =\\hfill &amp; \\text{interest}\\hfill \\\\ I=Prt\\hfill &amp; \\phantom{\\rule{1em}{0ex}}\\text{where}\\phantom{\\rule{1em}{0ex}}\\hfill &amp; P\\hfill &amp; =\\hfill &amp; \\text{principal}\\hfill \\\\ &amp; &amp; r\\hfill &amp; =\\hfill &amp; \\text{rate}\\hfill \\\\ &amp; &amp; t\\hfill &amp; =\\hfill &amp; \\text{time}\\hfill \\end{array}\\)<\/div><\/li><\/ul><\/div><div class=\"textbox\" data-depth=\"1\" id=\"fs-id1167836300510\"><div class=\"practice-perfect\" data-depth=\"2\" id=\"fs-id1167836300514\"><h4 data-type=\"title\">Practice Makes Perfect<\/h4><p id=\"fs-id1167836300522\"><strong data-effect=\"bold\">Use a Problem Solving Strategy for Word Problems<\/strong><\/p><div data-type=\"exercise\" id=\"fs-id1167833340063\"><div data-type=\"problem\" id=\"fs-id1167833340065\"><p id=\"fs-id1167833340068\">List five positive thoughts you can say to yourself that will help you approach word problems with a positive attitude. You may want to copy them on a sheet of paper and put it in the front of your notebook, where you can read them often.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836538791\"><p id=\"fs-id1167836538793\">Answers will vary.<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836538799\"><div data-type=\"problem\" id=\"fs-id1167829931415\"><p id=\"fs-id1167829931417\">List five negative thoughts that you have said to yourself in the past that will hinder your progress on word problems. You may want to write each one on a small piece of paper and rip it up to symbolically destroy the negative thoughts.<\/p><\/div><\/div><p id=\"fs-id1167836605126\">In the following exercises, solve using the problem solving strategy for word problems. Remember to write a complete sentence to answer each question.<\/p><div data-type=\"exercise\" id=\"fs-id1167836605131\"><div data-type=\"problem\" id=\"fs-id1167836605133\"><p id=\"fs-id1167836605135\">There are 16 girls in a school club. The number of girls is four more than twice the number of boys. Find the number of boys.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167833049947\"><p id=\"fs-id1167833049949\">six boys<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167833049954\"><div data-type=\"problem\" id=\"fs-id1167836649991\"><p id=\"fs-id1167836649993\">There are 18 Cub Scouts in Troop 645. The number of scouts is three more than five times the number of adult leaders. Find the number of adult leaders.<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167826170306\"><div data-type=\"problem\" id=\"fs-id1167826170308\"><p id=\"fs-id1167826170310\">Huong is organizing paperback and hardback books for her club\u2019s used book sale. The number of paperbacks is 12 less than three times the number of hardbacks. Huong had 162 paperbacks. How many hardback books were there?<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167826170315\"><p id=\"fs-id1167836493523\">58 hardback books<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836493529\"><div data-type=\"problem\" id=\"fs-id1167836416628\"><p id=\"fs-id1167836416630\">Jeff is lining up children\u2019s and adult bicycles at the bike shop where he works. The number of children\u2019s bicycles is nine less than three times the number of adult bicycles. There are 42 adult bicycles. How many children\u2019s bicycles are there?<\/p><\/div><\/div><p id=\"fs-id1167836624582\"><strong data-effect=\"bold\">Solve Number Word Problems<\/strong><\/p><p id=\"fs-id1167836624588\">In the following exercises, solve each number word problem.<\/p><div data-type=\"exercise\" id=\"fs-id1167836688863\"><div data-type=\"problem\" id=\"fs-id1167836688865\"><p id=\"fs-id1167836688867\">The difference of a number and 12 is three. Find the number.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836688871\"><p id=\"fs-id1167836688873\">15<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836321013\"><div data-type=\"problem\" id=\"fs-id1167836321015\"><p id=\"fs-id1167836321017\">The difference of a number and eight is four. Find the number.<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836363696\"><div data-type=\"problem\" id=\"fs-id1167836363698\"><p id=\"fs-id1167836363701\">The sum of three times a number and eight is 23. Find the number.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167833224664\"><p id=\"fs-id1167833224666\">5<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167833224672\"><div data-type=\"problem\" id=\"fs-id1167836433966\"><p id=\"fs-id1167836433968\">The sum of twice a number and six is 14. Find the number.<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829789166\"><div data-type=\"problem\" id=\"fs-id1167829789168\"><p>The difference of twice a number and seven is 17. Find the number.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167829789174\"><p id=\"fs-id1167829789176\">12<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167833047200\"><div data-type=\"problem\" id=\"fs-id1167833047202\"><p id=\"fs-id1167833047204\">The difference of four times a number and seven is 21. Find the number.<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167833328973\"><div data-type=\"problem\" id=\"fs-id1167833328975\"><p id=\"fs-id1167833328978\">Three times the sum of a number and nine is 12. Find the number.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836697750\"><p id=\"fs-id1167836697752\">\\(-5\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167832940609\"><div data-type=\"problem\" id=\"fs-id1167832940611\"><p id=\"fs-id1167832940614\">Six times the sum of a number and eight is 30. Find the number.<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167832994440\"><div data-type=\"problem\" id=\"fs-id1167832994442\"><p id=\"fs-id1167832994444\">One number is six more than the other. Their sum is 42. Find the numbers.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167829747774\"><p id=\"fs-id1167829747776\">18, 24<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829747782\"><div data-type=\"problem\" id=\"fs-id1167833386692\"><p id=\"fs-id1167833386694\">One number is five more than the other. Their sum is 33. Find the numbers.<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829590410\"><div data-type=\"problem\" id=\"fs-id1167829590412\"><p id=\"fs-id1167829590414\">The sum of two numbers is 20. One number is four less than the other. Find the numbers.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167829590419\"><p id=\"fs-id1167829590421\">8, 12<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829717297\"><div data-type=\"problem\" id=\"fs-id1167829717300\"><p id=\"fs-id1167829717302\">The sum of two numbers is 27. One number is seven less than the other. Find the numbers.<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836732384\"><div data-type=\"problem\" id=\"fs-id1167836732386\"><p id=\"fs-id1167833311250\">One number is 14 less than another. If their sum is increased by seven, the result is 85. Find the numbers.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167833311255\"><p id=\"fs-id1167833311257\">32, 46<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836730384\"><div data-type=\"problem\" id=\"fs-id1167836730386\"><p id=\"fs-id1167836730388\">One number is 11 less than another. If their sum is increased by eight, the result is 71. Find the numbers.<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167824732299\"><div data-type=\"problem\" id=\"fs-id1167824732301\"><p id=\"fs-id1167824732303\">The sum of two numbers is 14. One number is two less than three times the other. Find the numbers.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836610765\"><p id=\"fs-id1167836610767\">4, 10<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836610772\"><div data-type=\"problem\" id=\"fs-id1167836610774\"><p id=\"fs-id1167829843968\">The sum of two numbers is zero. One number is nine less than twice the other. Find the numbers.<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167833274532\"><div data-type=\"problem\" id=\"fs-id1167833274534\"><p id=\"fs-id1167833274536\">The sum of two consecutive integers is 77. Find the integers.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836610798\"><p id=\"fs-id1167836610800\">38, 39<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836610805\"><div data-type=\"problem\" id=\"fs-id1167833380167\"><p id=\"fs-id1167833380169\">The sum of two consecutive integers is 89. Find the integers.<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167826206362\"><div data-type=\"problem\" id=\"fs-id1167826206365\"><p id=\"fs-id1167826206367\">The sum of three consecutive integers is 78. Find the integers.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167826206371\"><p id=\"fs-id1167826206373\">25, 26, 27<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167833071653\"><div data-type=\"problem\" id=\"fs-id1167833071655\"><p id=\"fs-id1167833071657\">The sum of three consecutive integers is 60. Find the integers.<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167833240038\"><div data-type=\"problem\" id=\"fs-id1167833240040\"><p id=\"fs-id1167833240042\">Find three consecutive integers whose sum is \\(-36.\\)<\/p><\/div><div data-type=\"solution\"><p id=\"fs-id1167836546323\">\\(-11,-12,-13\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836507071\"><div data-type=\"problem\" id=\"fs-id1167836507073\"><p id=\"fs-id1167836507075\">Find three consecutive integers whose sum is \\(-3.\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836448552\"><div data-type=\"problem\" id=\"fs-id1167836508931\"><p id=\"fs-id1167836508933\">Find three consecutive even integers whose sum is 258.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836508938\"><p id=\"fs-id1167836508940\">84, 86, 88<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836415038\"><div data-type=\"problem\" id=\"fs-id1167836415040\"><p id=\"fs-id1167836415042\">Find three consecutive even integers whose sum is 222.<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836514322\"><div data-type=\"problem\" id=\"fs-id1167836514324\"><p id=\"fs-id1167836514326\">Find three consecutive odd integers whose sum is \\(-213.\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836408908\"><p id=\"fs-id1167836408910\">\\(-69,-71,-73\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836513517\"><div data-type=\"problem\" id=\"fs-id1167836513519\"><p id=\"fs-id1167836513521\">Find three consecutive odd integers whose sum is \\(-267.\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167833397290\"><div data-type=\"problem\" id=\"fs-id1167833397292\"><p id=\"fs-id1167836492064\">Philip pays ?1,620 in rent every month. This amount is ?120 more than twice what his brother Paul pays for rent. How much does Paul pay for rent?<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836492069\"><p id=\"fs-id1167836492072\">?750<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829853727\"><div data-type=\"problem\" id=\"fs-id1167829853729\"><p id=\"fs-id1167829853731\">Marc just bought an SUV for ?54,000. This is ?7,400 less than twice what his wife paid for her car last year. How much did his wife pay for her car?<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167824648796\"><div data-type=\"problem\" id=\"fs-id1167824648799\"><p id=\"fs-id1167824648801\">Laurie has ?46,000 invested in stocks and bonds. The amount invested in stocks is ?8,000 less than three times the amount invested in bonds. How much does Laurie have invested in bonds?<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167833224308\"><p id=\"fs-id1167833224310\">?13,500<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167833224315\"><div data-type=\"problem\" id=\"fs-id1167836665437\"><p id=\"fs-id1167836665439\">Erica earned a total of ?50,450 last year from her two jobs. The amount she earned from her job at the store was ?1,250 more than three times the amount she earned from her job at the college. How much did she earn from her job at the college?<\/p><\/div><\/div><p id=\"fs-id1167833020012\"><strong data-effect=\"bold\">Solve Percent Applications<\/strong><\/p><p id=\"fs-id1167833020018\">In the following exercises, translate and solve.<em data-effect=\"italics\"><\/em><\/p><div data-type=\"exercise\" id=\"fs-id1167836298448\"><div data-type=\"problem\" id=\"fs-id1167836298450\"><p id=\"fs-id1167836298453\"><span class=\"token\">\u24d0<\/span> What number is 45% of 120? <span class=\"token\">\u24d1<\/span> 81 is 75% of what number? <span class=\"token\">\u24d0<\/span> What percent of 260 is 78?<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836701016\"><p id=\"fs-id1167836701018\"><span class=\"token\">\u24d0<\/span> 54 <span class=\"token\">\u24d1<\/span> 108 <span class=\"token\">\u24d0<\/span> 30%<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829811784\"><div data-type=\"problem\" id=\"fs-id1167829811786\"><p id=\"fs-id1167829811788\"><span class=\"token\">\u24d0<\/span> What number is 65% of 100? <span class=\"token\">\u24d1<\/span> 93 is 75% of what number? <span class=\"token\">\u24d0<\/span> What percent of 215 is 86?<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829878304\"><div data-type=\"problem\" id=\"fs-id1167829878306\"><p id=\"fs-id1167829878308\"><span class=\"token\">\u24d0<\/span> 250% of 65 is what number? <span class=\"token\">\u24d1<\/span> 8.2% of what amount is ?2.87? <span class=\"token\">\u24d0<\/span> 30 is what percent of 20?<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836704536\"><p id=\"fs-id1167836704538\"><span class=\"token\">\u24d0<\/span>\\(162.5\\)<span class=\"token\">\u24d1<\/span> ?35 <span class=\"token\">\u24d0<\/span> 150%<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167833058040\"><div data-type=\"problem\" id=\"fs-id1167833058042\"><p id=\"fs-id1167833058044\"><span class=\"token\">\u24d0<\/span> 150% of 90 is what number? <span class=\"token\">\u24d1<\/span> 6.4% of what amount is ?2.88? <span class=\"token\">\u24d0<\/span> 50 is what percent of 40?<\/p><\/div><\/div><p id=\"fs-id1167829919871\">In the following exercises, solve.<\/p><div data-type=\"exercise\" id=\"fs-id1167829919874\"><div data-type=\"problem\" id=\"fs-id1167829919876\"><p id=\"fs-id1167829919878\">Geneva treated her parents to dinner at their favorite restaurant. The bill was ?74.25. Geneva wants to leave 16% of the total bill as a tip. How much should the tip be?<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167829693632\"><p id=\"fs-id1167836611999\">\\(\\text{?}11.88\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836612010\"><div data-type=\"problem\" id=\"fs-id1167832999766\"><p id=\"fs-id1167832999768\">When Hiro and his co-workers had lunch at a restaurant near their work, the bill was ?90.50. They want to leave 18% of the total bill as a tip. How much should the tip be?<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167833227165\"><div data-type=\"problem\" id=\"fs-id1167833227167\"><p id=\"fs-id1167833227169\">One serving of oatmeal has 8 grams of fiber, which is 33% of the recommended daily amount. What is the total recommended daily amount of fiber?<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836322669\"><p id=\"fs-id1167836322671\">24.2 g<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836322677\"><div data-type=\"problem\" id=\"fs-id1167836322679\"><p id=\"fs-id1167829691106\">One serving of trail mix has 67 grams of carbohydrates, which is 22% of the recommended daily amount. What is the total recommended daily amount of carbohydrates?<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836576424\"><div data-type=\"problem\" id=\"fs-id1167836576426\"><p id=\"fs-id1167836576428\">A bacon cheeseburger at a popular fast food restaurant contains 2070 milligrams (mg) of sodium, which is 86% of the recommended daily amount. What is the total recommended daily amount of sodium?<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836476709\"><p id=\"fs-id1167836476711\">2407 mg<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836476716\"><div data-type=\"problem\" id=\"fs-id1167836476718\"><p id=\"fs-id1167836602310\">A grilled chicken salad at a popular fast food restaurant contains 650 milligrams (mg) of sodium, which is 27% of the recommended daily amount. What is the total recommended daily amount of sodium?<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167832940653\"><div data-type=\"problem\" id=\"fs-id1167832940655\"><p id=\"fs-id1167832940657\">The nutrition fact sheet at a fast food restaurant says the fish sandwich has 380 calories, and 171 calories are from fat. What percent of the total calories is from fat?<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167832940663\"><p id=\"fs-id1167829756388\">45%<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829756393\"><div data-type=\"problem\" id=\"fs-id1167829756395\"><p id=\"fs-id1167829756398\">The nutrition fact sheet at a fast food restaurant says a small portion of chicken nuggets has 190 calories, and 114 calories are from fat. What percent of the total calories is from fat?<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836319645\"><div data-type=\"problem\" id=\"fs-id1167836667015\"><p id=\"fs-id1167836667017\">Emma gets paid ?3,000 per month. She pays ?750 a month for rent. What percent of her monthly pay goes to rent?<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836667022\"><p id=\"fs-id1167836667024\">25%<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836618689\"><div data-type=\"problem\" id=\"fs-id1167836618692\"><p id=\"fs-id1167836618694\">Dimple gets paid ?3,200 per month. She pays ?960 a month for rent. What percent of her monthly pay goes to rent?<\/p><\/div><\/div><p id=\"fs-id1167836554347\">In the following exercises, solve.<\/p><div data-type=\"exercise\" id=\"fs-id1167836554350\"><div data-type=\"problem\" id=\"fs-id1167836554352\"><p id=\"fs-id1167829893903\">Tamanika received a raise in her hourly pay, from ?15.50 to ?17.36. Find the percent change.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167829624095\"><p id=\"fs-id1167829595401\">12%<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829595406\"><div data-type=\"problem\" id=\"fs-id1167829595408\"><p id=\"fs-id1167829595410\">Ayodele received a raise in her hourly pay, from ?24.50 to ?25.48. Find the percent change.<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829695315\"><div data-type=\"problem\" id=\"fs-id1167829695317\"><p id=\"fs-id1167829695319\">Annual student fees at the University of California rose from about ?4,000 in 2000 to about ?12,000 in 2010. Find the percent change.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167829695325\"><p id=\"fs-id1167836521072\">200%<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836521077\"><div data-type=\"problem\" id=\"fs-id1167836521079\"><p id=\"fs-id1167836521081\">The price of a share of one stock rose from ?12.50 to ?50. Find the percent change.<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167833350404\"><div data-type=\"problem\" id=\"fs-id1167833350406\"><p id=\"fs-id1167833350408\">A grocery store reduced the price of a loaf of bread from ?2.80 to ?2.73. Find the percent change.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167829755991\"><p id=\"fs-id1167829755993\">\\(-2.5%\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836531527\"><div data-type=\"problem\" id=\"fs-id1167836531529\"><p id=\"fs-id1167836531531\">The price of a share of one stock fell from ?8.75 to ?8.54. Find the percent change.<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167826211784\"><div data-type=\"problem\" id=\"fs-id1167826211786\"><p id=\"fs-id1167826211788\">Hernando\u2019s salary was ?49,500 last year. This year his salary was cut to ?44,055. Find the percent change.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167833052534\"><p id=\"fs-id1167833052537\">\\(-11%\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836576058\"><div data-type=\"problem\" id=\"fs-id1167836576060\"><p id=\"fs-id1167836576062\">In ten years, the population of Detroit fell from 950,000 to about 712,500. Find the percent change.<\/p><\/div><\/div><p id=\"fs-id1167829721247\">In the following exercises, find <span class=\"token\">\u24d0<\/span> the amount of discount and <span class=\"token\">\u24d1<\/span> the sale price.<\/p><div data-type=\"exercise\" id=\"fs-id1167829740266\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167829740268\"><p id=\"fs-id1167836531586\">Janelle bought a beach chair on sale at 60% off. The original price was ?44.95.<\/p><\/div><div data-type=\"solution\"><p id=\"fs-id1167836541940\"><span class=\"token\">\u24d0<\/span>\\(\\text{?}26.97\\)<span class=\"token\">\u24d1<\/span>\\(\\text{?}17.98\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829752238\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167829752241\"><p id=\"fs-id1167829752243\">Errol bought a skateboard helmet on sale at 40% off. The original price was ?49.95.<\/p><\/div><\/div><p id=\"fs-id1167829691157\">In the following exercises, find <span class=\"token\">\u24d0<\/span> the amount of discount and <span class=\"token\">\u24d1<\/span> the discount rate (Round to the nearest tenth of a percent if needed.)<\/p><div data-type=\"exercise\" id=\"fs-id1167829595570\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167829595572\"><p id=\"fs-id1167836449693\">Larry and Donna bought a sofa at the sale price of ?1,344. The original price of the sofa was ?1,920.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836449697\"><p id=\"fs-id1167836449700\"><span class=\"token\">\u24d0<\/span> ?576 <span class=\"token\">\u24d1<\/span> 30%<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829811898\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167829811900\"><p id=\"fs-id1167829811902\">Hiroshi bought a lawnmower at the sale price of ?240. The original price of the lawnmower is ?300.<\/p><\/div><\/div><p id=\"fs-id1167832937184\">In the following exercises, find <span class=\"token\">\u24d0<\/span> the amount of the mark-up and <span class=\"token\">\u24d1<\/span> the list price.<\/p><div data-type=\"exercise\" id=\"fs-id1167832999647\"><div data-type=\"problem\" id=\"fs-id1167832999649\"><p id=\"fs-id1167832999651\">Daria bought a bracelet at original cost ?16 to sell in her handicraft store. She marked the price up 45%. What was the list price of the bracelet?<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836535896\"><p id=\"fs-id1167836535898\"><span class=\"token\">\u24d0<\/span>\\(\\text{?}7.20\\)<span class=\"token\">\u24d1<\/span>\\(\\text{?}23.20\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167824734807\"><div data-type=\"problem\" id=\"fs-id1167824734809\"><p id=\"fs-id1167824734811\">Regina bought a handmade quilt at original cost ?120 to sell in her quilt store. She marked the price up 55%. What was the list price of the quilt?<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836700655\"><div data-type=\"problem\" id=\"fs-id1167836700657\"><p id=\"fs-id1167836700660\">Tom paid ?0.60 a pound for tomatoes to sell at his produce store. He added a 33% mark-up. What price did he charge his customers for the tomatoes?<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836621799\"><p id=\"fs-id1167833057683\"><span class=\"token\">\u24d0<\/span>\\(\\text{?}0.20\\)<span class=\"token\">\u24d1<\/span>\\(\\text{?}0.80\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167833346738\"><div data-type=\"problem\" id=\"fs-id1167833346740\"><p id=\"fs-id1167833346742\">Flora paid her supplier ?0.74 a stem for roses to sell at her flower shop. She added an 85% mark-up. What price did she charge her customers for the roses?<\/p><\/div><\/div><p id=\"fs-id1167833310740\"><strong data-effect=\"bold\">Solve Simple Interest Applications<\/strong><em data-effect=\"italics\"><\/em><\/p><p id=\"fs-id1167833310749\">In the following exercises, solve.<\/p><div data-type=\"exercise\" id=\"fs-id1167829879268\"><div data-type=\"problem\" id=\"fs-id1167829879270\"><p id=\"fs-id1167829879273\">Casey deposited ?1,450 in a bank account that earned simple interest at an interest rate of 4%. How much interest was earned in two years?<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167829879278\"><p id=\"fs-id1167829879280\">?116<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836551570\"><div data-type=\"problem\" id=\"fs-id1167836551572\"><p id=\"fs-id1167836551574\">Terrence deposited ?5,720 in a bank account that earned simple interest at an interest rate of 6%. How much interest was earned in four years?<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167833054990\"><div data-type=\"problem\" id=\"fs-id1167833054992\"><p id=\"fs-id1167836387520\">Robin deposited ?31,000 in a bank account that earned simple interest at an interest rate of 5.2%. How much interest was earned in three years?<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836387526\"><p id=\"fs-id1167836387528\">?4836<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829785461\"><div data-type=\"problem\" id=\"fs-id1167829785463\"><p id=\"fs-id1167829785465\">Carleen deposited ?16,400 in a bank account that earned simple interest at an interest rate of 3.9% How much interest was earned in eight years?<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836575190\"><div data-type=\"problem\" id=\"fs-id1167836575192\"><p id=\"fs-id1167826206379\">Hilaria borrowed ?8,000 from her grandfather to pay for college. Five years later, she paid him back the ?8,000, plus ?1,200 interest. What was the rate of simple interest?<\/p><\/div><div data-type=\"solution\"><p id=\"fs-id1167826206387\">3%<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167833369027\"><div data-type=\"problem\" id=\"fs-id1167833369029\"><p id=\"fs-id1167833369031\">Kenneth lent his niece ?1,200 to buy a computer. Two years later, she paid him back the ?1,200, plus ?96 interest. What was the rate of simple interest?<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836391228\"><div data-type=\"problem\" id=\"fs-id1167836391230\"><p id=\"fs-id1167836391232\">Lebron lent his daughter ?20,000 to help her buy a condominium. When she sold the condominium four years later, she paid him the ?20,000, plus ?3,000 interest. What was the rate of simple interest?<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836598890\"><p id=\"fs-id1167836598892\">\\(3.75%\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829790280\"><div data-type=\"problem\" id=\"fs-id1167829790282\"><p id=\"fs-id1167829790285\">Pablo borrowed ?50,000 to start a business. Three years later, he repaid the ?50,000, plus ?9,375 interest. What was the rate of simple interest?<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167826171978\"><div data-type=\"problem\" id=\"fs-id1167826146791\"><p id=\"fs-id1167826146793\">In 10 years, a bank account that paid 5.25% simple interest earned ?18,375 interest. What was the principal of the account?<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836605943\"><p id=\"fs-id1167836605946\">?35,000<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836605951\"><div data-type=\"problem\" id=\"fs-id1167836605953\"><p id=\"fs-id1167836529597\">In 25 years, a bond that paid 4.75% simple interest earned ?2,375 interest. What was the principal of the bond?<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167832930332\"><div data-type=\"problem\" id=\"fs-id1167832930334\"><p id=\"fs-id1167832930336\">Joshua\u2019s computer loan statement said he would pay ?1,244.34 in simple interest for a three-year loan at 12.4%. How much did Joshua borrow to buy the computer?<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836580097\"><p id=\"fs-id1167836580099\">?3345<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836580104\"><div data-type=\"problem\" id=\"fs-id1167836580106\"><p id=\"fs-id1167829754765\">Margaret\u2019s car loan statement said she would pay ?7,683.20 in simple interest for a five-year loan at 9.8%. How much did Margaret borrow to buy the car?<\/p><\/div><\/div><\/div><div class=\"everyday\" data-depth=\"2\" id=\"fs-id1167833347102\"><h4 data-type=\"title\">Everyday Math<\/h4><div data-type=\"exercise\" id=\"fs-id1167833347108\"><div data-type=\"problem\" id=\"fs-id1167829741376\"><p id=\"fs-id1167829741378\"><strong data-effect=\"bold\">Tipping<\/strong> At the campus coffee cart, a medium coffee costs ?1.65. MaryAnne brings ?2.00 with her when she buys a cup of coffee and leaves the change as a tip. What percent tip does she leave?<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167833349758\"><p id=\"fs-id1167833349760\">\\(17.5%\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167833082221\"><div data-type=\"problem\" id=\"fs-id1167833082223\"><p id=\"fs-id1167833082225\"><strong data-effect=\"bold\">Tipping<\/strong> Four friends went out to lunch and the bill came to ?53.75 They decided to add enough tip to make a total of ?64, so that they could easily split the bill evenly among themselves. What percent tip did they leave?<\/p><\/div><\/div><\/div><div class=\"writing\" data-depth=\"2\" id=\"fs-id1167833385993\"><h4 data-type=\"title\">Writing Exercises<\/h4><div data-type=\"exercise\" id=\"fs-id1167833385999\"><div data-type=\"problem\" id=\"fs-id1167833386001\"><p id=\"fs-id1167833386004\">What has been your past experience solving word problems? Where do you see yourself moving forward?<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167829850147\"><p id=\"fs-id1167829850149\">Answers will vary.<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829850154\"><div data-type=\"problem\" id=\"fs-id1167829850156\"><p id=\"fs-id1167836515997\">Without solving the problem \u201c44 is 80% of what number\u201d think about what the solution might be. Should it be a number that is greater than 44 or less than 44? Explain your reasoning.<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836516006\"><div data-type=\"problem\" id=\"fs-id1167836516008\"><p id=\"fs-id1167836630152\">After returning from vacation, Alex said he should have packed 50% fewer shorts and 200% more shirts. Explain what Alex meant.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836630157\"><p id=\"fs-id1167836630159\">Answers will vary.<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836610897\"><div data-type=\"problem\" id=\"fs-id1167836610899\"><p id=\"fs-id1167836610901\">Because of road construction in one city, commuters were advised to plan that their Monday morning commute would take 150% of their usual commuting time. Explain what this means.<\/p><\/div><\/div><\/div><div class=\"bc-section section\" data-depth=\"2\" id=\"fs-id1167836527743\"><h4 data-type=\"title\">Self Check<\/h4><p id=\"fs-id1167836692505\"><span class=\"token\">\u24d0<\/span> After completing the exercises, use this checklist to evaluate your mastery of the objective of this section.<\/p><span data-type=\"media\" id=\"fs-id1167836692516\" data-alt=\"This table has four columns and five rows. The first row is a header and it labels each column, \u201cI can\u2026\u201d, \u201cConfidently,\u201d \u201cWith some help,\u201d and \u201cNo-I don\u2019t get it!\u201d In row 2, the I can was use a problem-solving strategy for word problems. In row 3, the I can was solve number problems. In row 4, the I can was solve percent applications. In row 5, the I can was solve simple interest applications.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_201_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This table has four columns and five rows. The first row is a header and it labels each column, \u201cI can\u2026\u201d, \u201cConfidently,\u201d \u201cWith some help,\u201d and \u201cNo-I don\u2019t get it!\u201d In row 2, the I can was use a problem-solving strategy for word problems. In row 3, the I can was solve number problems. In row 4, the I can was solve percent applications. In row 5, the I can was solve simple interest applications.\"><\/span><p><span class=\"token\">\u24d1<\/span> After reviewing this checklist, what will you do to become confident for all objectives?<\/p><\/div><\/div>\n","rendered":"<div class=\"textbox textbox--learning-objectives\">\n<h3 itemprop=\"educationalUse\">Learning Objectives<\/h3>\n<p>By the end of this section, you will be able to: <\/p>\n<ul>\n<li>Use a problem solving strategy for word problems<\/li>\n<li>Solve number word problems<\/li>\n<li>Solve percent applications<\/li>\n<li>Solve simple interest applications<\/li>\n<\/ul>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167836288591\" class=\"be-prepared\">\n<p id=\"fs-id1167836356925\">Before you get started, take this readiness quiz.<\/p>\n<ol id=\"fs-id1167836543609\" type=\"1\">\n<li>Translate \u201csix less than twice <em data-effect=\"italics\">x<\/em>\u201d into an algebraic expression.\n<div data-type=\"newline\"><\/div>\n<p> If you missed this problem, review <a href=\"\/contents\/d3697553-3900-453f-8c08-8f74d55711ba#fs-id1167836513192\" class=\"autogenerated-content\">(Figure)<\/a>.<\/li>\n<li>Convert 4.5% to a decimal.\n<div data-type=\"newline\"><\/div>\n<p> If you missed this problem, review <a href=\"\/contents\/99b2296a-9957-4380-aff4-248abadc862b#fs-id1167829721053\" class=\"autogenerated-content\">(Figure)<\/a>.<\/li>\n<li>Convert 0.6 to a percent.\n<div data-type=\"newline\"><\/div>\n<p> If you missed this problem, review <a href=\"\/contents\/99b2296a-9957-4380-aff4-248abadc862b#fs-id1167829721053\" class=\"autogenerated-content\">(Figure)<\/a>.<\/li>\n<\/ol>\n<\/div>\n<p id=\"fs-id1167833223914\">Have you ever had any negative experiences in the past with word problems? When we feel we have no control, and continue repeating negative thoughts, we set up barriers to success. Realize that your negative experiences with word problems are in your past. To move forward you need to calm your fears and change your negative feelings.<\/p>\n<p id=\"fs-id1167829599677\">Start with a fresh slate and begin to think positive thoughts. Repeating some of the following statements may be helpful to turn your thoughts positive. Thinking positive thoughts is a first step towards success.<\/p>\n<p id=\"fs-id1166401559623\">\u2003\u2003I think I can! I think I can!<\/p>\n<p id=\"fs-id1167836544756\">\u2003\u2003While word problems were hard in the past, I think I can try them now.<\/p>\n<p id=\"fs-id1167836551851\">\u2003\u2003I am better prepared now\u2014I think I will begin to understand word problems.<\/p>\n<p id=\"fs-id1167836379098\">\u2003\u2003I am able to solve equations because I practiced many problems and I got help when I needed it\u2014I can try that<\/p>\n<div data-type=\"newline\"><\/div>\n<p>\u2003\u2003with word problems.<\/p>\n<p id=\"fs-id1167833055883\">\u2003\u2003It may take time, but I can begin to solve word problems.<\/p>\n<p id=\"fs-id1167833224302\">You are now well prepared and you are ready to succeed. If you take control and believe you can be successful, you will be able to master word problems.<\/p>\n<div class=\"bc-section section\" data-depth=\"1\" id=\"fs-id1167836607409\">\n<h3 data-type=\"title\">Use a Problem Solving Strategy for Word Problems<\/h3>\n<p id=\"fs-id1167836688094\">Now that we can solve equations, we are ready to apply our new skills to word problems. We will develop a strategy we can use to solve any word problem successfully.<\/p>\n<div data-type=\"example\" id=\"fs-id1167833053847\" class=\"textbox textbox--examples\">\n<div data-type=\"exercise\" id=\"fs-id1167836528531\">\n<div data-type=\"problem\" id=\"fs-id1167836293464\">\n<p id=\"fs-id1167836387267\">Normal yearly snowfall at the local ski resort is 12 inches more than twice the amount it received last season. The normal yearly snowfall is 62 inches. What was the snowfall last season at the ski resort?<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167833097195\">\n<table id=\"fs-id1167829809695\" class=\"unnumbered unstyled can-break\" summary=\"Step 1 is to read the problem. Step 2 is to identify what you are looking for. What was the snowfall last season? Step 3 is to name what we are looking for and choose a variable to represent it. Let s be equal to the snowfall last season. Step 4 is to translate. Restate the problem in one sentence with all the important information. The normal snowfall is 62, was is the equals sign, and twelve more than twice the amount last year is 2 s plus 12. The equation is 62 is equal to 2 s plus 12. Step 5 is to solve the equation. Subtract 12 from each side. The result is 62 minus 12 is equal to 2 s plus 12 minus 12. Simplify. The result is 50 is equal to 2 s. Divide each side by 2. The result is 50 divided by 2 is equal to 2 s divided by 2. Simplify. The result is 25 is equal to s. Step 6 is to check the solution. First is our answer reasonable? Yes, having 25 inches of snow seems OK. The problem says the normal snowfall is twelve inches more than twice the number of last season. Twice 25 is 50 and 12 more than that is 62. Step 7 is to answer the question. The snowfall last season was 25 inches.\" data-label=\"\">\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 1. Read<\/strong> the problem.<\/td>\n<td><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 2. Identify<\/strong> what you are looking for.<\/td>\n<td data-valign=\"top\" data-align=\"left\">What was the snowfall last season?<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 3. Name<\/strong> what we are looking for and<\/p>\n<div data-type=\"newline\"><\/div>\n<p>choose a variable to represent it.<\/td>\n<td data-valign=\"top\" data-align=\"left\">Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-12ac9f5dee0c0d9acdb247ec52211d05_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#115;&#61;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"26\" style=\"vertical-align: 0px;\" \/> the snowfall last season.<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 4. Translate.<\/strong><\/p>\n<div data-type=\"newline\"><\/div>\n<p>Restate the problem in one sentence with all the important information.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836700619\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_001a_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Translate into an equation.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836355755\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_001b_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 5. Solve<\/strong> the equation.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836448458\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_001c_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Subtract 12 from each side.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836448581\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_001d_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Simplify.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167833057954\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_001e_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Divide each side by two.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836694120\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_001f_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Simplify.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836596014\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_001g_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td colspan=\"2\" data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 6. Check:<\/strong> First, is our answer reasonable?<\/p>\n<div data-type=\"newline\"><\/div>\n<p>Yes, having 25 inches of snow seems OK.<\/p>\n<div data-type=\"newline\"><\/div>\n<p>The problem says the normal snowfall is twelve<\/p>\n<div data-type=\"newline\"><\/div>\n<p>inches more than twice the number of last season.<\/p>\n<div data-type=\"newline\"><\/div>\n<p>Twice 25 is 50 and 12 more than that is 62.<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 7. Answer<\/strong> the question.<\/td>\n<td data-valign=\"top\" data-align=\"left\">The snowfall last season was 25 inches.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167836292778\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167829742302\">\n<div data-type=\"problem\" id=\"fs-id1167829598115\">\n<p id=\"fs-id1167829719164\">Guillermo bought textbooks and notebooks at the bookstore. The number of textbooks was three more than twice the number of notebooks. He bought seven textbooks. How many notebooks did he buy?<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836326498\">\n<p id=\"fs-id1167833361713\">He bought two notebooks.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167829756413\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167826170319\">\n<div data-type=\"problem\" id=\"fs-id1167833055336\">\n<p id=\"fs-id1167836492140\">Gerry worked Sudoku puzzles and crossword puzzles this week. The number of Sudoku puzzles he completed is eight more than twice the number of crossword puzzles. He completed 22 Sudoku puzzles. How many crossword puzzles did he do?<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836701489\">\n<p id=\"fs-id1167836288517\">He did seven crosswords puzzles.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1167836551928\">We summarize an effective strategy for problem solving.<\/p>\n<div data-type=\"note\" id=\"fs-id1167836407180\" class=\"howto\">\n<div data-type=\"title\">Use a Problem Solving Strategy for word problems.<\/div>\n<ol id=\"fs-id1167836287137\" type=\"1\" class=\"stepwise\">\n<li><strong data-effect=\"bold\">Read<\/strong> the problem. Make sure all the words and ideas are understood.<\/li>\n<li><strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/li>\n<li><strong data-effect=\"bold\">Name<\/strong> what you are looking for. Choose a variable to represent that quantity.<\/li>\n<li><strong data-effect=\"bold\">Translate<\/strong> into an equation. It may be helpful to restate the problem in one sentence with all the important information. Then, translate the English sentence into an algebra equation.<\/li>\n<li><strong data-effect=\"bold\">Solve<\/strong> the equation using proper algebra techniques.<\/li>\n<li><strong data-effect=\"bold\">Check<\/strong> the answer in the problem to make sure it makes sense.<\/li>\n<li><strong data-effect=\"bold\">Answer<\/strong> the question with a complete sentence.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<div class=\"bc-section section\" data-depth=\"1\">\n<h3 data-type=\"title\">Solve Number Word Problems<\/h3>\n<p id=\"fs-id1167836722637\">We will now apply the problem solving strategy to \u201cnumber word problems.\u201d Number word problems give some clues about one or more numbers and we use these clues to write an equation. Number word problems provide good practice for using the Problem Solving Strategy.<\/p>\n<div data-type=\"example\" id=\"fs-id1167836525150\" class=\"textbox textbox--examples\">\n<div data-type=\"exercise\" id=\"fs-id1167833311015\">\n<div data-type=\"problem\" id=\"fs-id1167833050789\">\n<p id=\"fs-id1167836415272\">The sum of seven times a number and eight is thirty-six. Find the number.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836623937\">\n<table id=\"fs-id1167836612346\" class=\"unnumbered unstyled can-break\" summary=\"Did you notice that we left out some of the steps as we solved this equation? If you\u2019re not yet ready to leave out these steps, write down as many as you need. Step 1 is to read the problem. Step 2 is to identify what you are looking for. It is the number. Step 3 is name what you are look for and choose a variable to represent it. Let be equal to the number. Step 4 is to translate. Restate the problem as one sentence. The sum of seven times a number and 8 is 7 n plus 8, is the equals sign, and 36 is 36. Translate into an equation. The equation is 7 n plus 8 is equal to 36. Step 5 is to solve the equation. Subtract 7 from each side and simplify. The result is 7 n is equal to 28. Divide each side by 2 and simplify. The result is n is equal to 4. Step 6 is to check the solution. Is the sum of 7 times 4 plus 8 equal to 36? Is 28 plus 8 equal to 36? 36 is equal to 36. The solution checks. Step 7 is to answer the question. The number is 4.\" data-label=\"\">\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 1. Read<\/strong> the problem.<\/td>\n<td><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 2. Identify<\/strong> what you are looking for.<\/td>\n<td data-valign=\"top\" data-align=\"left\">the number<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 3. Name<\/strong> what you are looking for and<\/p>\n<div data-type=\"newline\"><\/div>\n<p>choose a variable to represent it.<\/td>\n<td data-valign=\"top\" data-align=\"left\">Let <em data-effect=\"italics\">n<\/em> = the number.<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 4. Translate:<\/strong><\/p>\n<div data-type=\"newline\"><\/div>\n<p>Restate the problem as one sentence.<\/p>\n<div data-type=\"newline\"><\/div>\n<p>Translate into an equation.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836691731\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_002a_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167836539753\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_002b_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 5. Solve<\/strong> the equation.<\/p>\n<div data-type=\"newline\"><\/div>\n<p>Subtract eight from each side and simplify.<\/p>\n<div data-type=\"newline\"><\/div>\n<p>Divide each side by seven and simplify.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836391366\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_002c_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167832945886\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_002d_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167832999844\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_002e_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 6. Check.<\/strong><\/p>\n<div data-type=\"newline\"><\/div>\n<p>Is the sum of seven times four plus eight equal to 36?<\/p>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-b5b97aa46ab78cfc54db686b58557657_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#55;&middot;&#52;&#43;&#56;&#38;&#32;&#92;&#115;&#116;&#97;&#99;&#107;&#114;&#101;&#108;&#123;&#63;&#125;&#123;&#61;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#51;&#54;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#50;&#56;&#43;&#56;&#38;&#32;&#92;&#115;&#116;&#97;&#99;&#107;&#114;&#101;&#108;&#123;&#63;&#125;&#123;&#61;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#51;&#54;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#51;&#54;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#51;&#54;&#10003;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"68\" width=\"112\" style=\"vertical-align: -27px;\" \/><\/td>\n<td><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 7. Answer<\/strong> the question.<\/td>\n<td data-valign=\"top\" data-align=\"left\">The number is 4.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1167829748097\">Did you notice that we left out some of the steps as we solved this equation? If you\u2019re not yet ready to leave out these steps, write down as many as you need.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167829693799\">\n<div data-type=\"problem\" id=\"fs-id1167833059816\">\n<p id=\"fs-id1167833369771\">The sum of four times a number and two is fourteen. Find the number.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167833021343\">\n<p id=\"fs-id1167836550075\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-4a1d3ea4963f568cabd97329456036b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167829906315\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167829580384\">\n<div data-type=\"problem\" id=\"fs-id1167829691197\">\n<p id=\"fs-id1167836520333\">The sum of three times a number and seven is twenty-five. Find the number.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836537101\">\n<p id=\"fs-id1167833057967\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-b5c3e12330dabaeec7413281aba0f134_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1167836327026\">Some number word problems ask us to find two or more numbers. It may be tempting to name them all with different variables, but so far, we have only solved equations with one variable. In order to avoid using more than one variable, we will define the numbers in terms of the same variable. Be sure to read the problem carefully to discover how all the numbers relate to each other.<\/p>\n<div data-type=\"example\" id=\"fs-id1167829754000\" class=\"textbox textbox--examples\">\n<div data-type=\"exercise\" id=\"fs-id1167836620984\">\n<div data-type=\"problem\" id=\"fs-id1167836538090\">\n<p id=\"fs-id1167836449474\">The sum of two numbers is negative fifteen. One number is nine less than the other. Find the numbers.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836534850\">\n<table id=\"fs-id1167836312913\" class=\"unnumbered unstyled can-break\" summary=\"Step 1 is to read the problem. Step 2 is identify what you are looking for. It is two numbers. Step 3 is to name what you are looking for by choosing a variable to represent the first number. Let n be equal to the first number. One number is 9 less than the other. Let n minus 9 be equal to the second number. Step 4 is to translate. Write the sum of two numbers is negative 15. That is the first number plus the second number is negative 15. Translate it into an equation. The equation is n plus the quantity n minus 9 is equal to negative 15. Step 5 is to solve the equation. Combine like terms. The result is 2 n minus 9 is equal to negative 15. Add 9 to each side and simplify. The result is 2 n is equal to negative 6. Simplify. The result is n is equal negative 3, which is the first number. The expression, n minus 9, is the second number. Negative 3 minus 9 is negative 12. Step 6 is to check the solutions. Is negative 12 nine less than negative 3? Is negative 3 minus 9 equal to negative 12? Is negative 12 equal to negative 12? Is their sum negative 15? Is negative 3 plus negative 12 equal to negative 15? Negative 15 is equal to negative 15. The solutions check. Step 7 is to answer the question. The numbers are negative 3 and negative 12.\" data-label=\"\">\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 1. Read<\/strong> the problem.<\/td>\n<td><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 2. Identify<\/strong> what you are looking for.<\/td>\n<td data-valign=\"top\" data-align=\"left\">two numbers<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 3. Name<\/strong> what you are looking for by<\/p>\n<div data-type=\"newline\"><\/div>\n<p>choosing a variable to represent the first<\/p>\n<div data-type=\"newline\"><\/div>\n<p>number.<\/p>\n<div data-type=\"newline\"><\/div>\n<p>\u201cOne number is nine less than the other.\u201d<\/td>\n<td data-valign=\"top\" data-align=\"left\">\n<div data-type=\"newline\"><\/div>\n<p>Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-b734576de3bec67d4cc5191e0e847674_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#61;&#123;&#49;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#116;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"53\" style=\"vertical-align: -1px;\" \/> number.<\/p>\n<div data-type=\"newline\"><\/div>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-496ff0b014a86a034106707fd87659c3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#45;&#57;&#61;&#123;&#50;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#110;&#100;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"90\" style=\"vertical-align: 0px;\" \/> number<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 4. Translate.<\/strong><\/p>\n<div data-type=\"newline\"><\/div>\n<p>Write as one sentence.<\/p>\n<div data-type=\"newline\"><\/div>\n<p>Translate into an equation.<\/td>\n<td data-valign=\"top\" data-align=\"left\">\n<div data-type=\"newline\"><\/div>\n<p>The sum of two numbers is negative fifteen.<\/p>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167836287362\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_003a_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 5. Solve<\/strong> the equation.<\/p>\n<div data-type=\"newline\"><\/div>\n<p>Combine like terms.<\/p>\n<div data-type=\"newline\"><\/div>\n<p>Add nine to each side and simplify.<\/p>\n<div data-type=\"newline\"><\/div>\n<p>Simplify.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836415072\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_003b_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167829691498\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_003c_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167832999705\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_003d_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167836646293\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_003e_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167836732526\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_003f_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167833385719\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_003g_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_003h_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 6. Check.<\/strong><\/p>\n<div data-type=\"newline\"><\/div>\n<p>Is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-9eae543c53f9301fa411ef541a1f4433_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"30\" style=\"vertical-align: -1px;\" \/> nine less than <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-80cc5c6a8396c9c51a989af972cef479_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#63;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"30\" style=\"vertical-align: 0px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-37c75299c5fc38efdc57e895ed8aaf25_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#45;&#51;&#45;&#57;&#38;&#32;&#92;&#115;&#116;&#97;&#99;&#107;&#114;&#101;&#108;&#123;&#63;&#125;&#123;&#61;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#45;&#49;&#50;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#45;&#49;&#50;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#45;&#49;&#50;&#10003;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"129\" style=\"vertical-align: -15px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p>Is their sum <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-9223bf414c099aed9f34fe9dd4e1a913_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#53;&#63;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"39\" style=\"vertical-align: -1px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-b1cb8c04ed02a1c1c9fd5f1692a646ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#45;&#51;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#38;&#32;&#92;&#115;&#116;&#97;&#99;&#107;&#114;&#101;&#108;&#123;&#63;&#125;&#123;&#61;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#45;&#49;&#53;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#45;&#49;&#53;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#45;&#49;&#53;&#10003;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"165\" style=\"vertical-align: -15px;\" \/><\/td>\n<td><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 7. Answer<\/strong> the question.<\/td>\n<td data-valign=\"top\" data-align=\"left\">The numbers are <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-470cb162cf92c55d139f4f69216225e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-d2403419a9846266a1686ba8ae7385e4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#50;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"35\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167829832950\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167836363791\">\n<div data-type=\"problem\" id=\"fs-id1167836685299\">\n<p id=\"fs-id1167836288208\">The sum of two numbers is negative twenty-three. One number is seven less than the other. Find the numbers.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167829644871\">\n<p id=\"fs-id1167836391362\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-08a6420a7f2009801f497c63ee38a72e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#53;&#44;&#45;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"61\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167833055971\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167830122597\">\n<div data-type=\"problem\" id=\"fs-id1167833058214\">\n<p id=\"fs-id1167833060864\">The sum of two numbers is negative eighteen. One number is forty more than the other. Find the numbers.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167829694885\">\n<p id=\"fs-id1167829627465\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-562c7a428b60e681465f834e50c30f83_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#57;&#44;&#49;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"55\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1167833412513\">Some number problems involve <strong data-effect=\"bold\">consecutive integers<\/strong>. Consecutive integers are integers that immediately follow each other. Examples of <span data-type=\"term\">consecutive integers<\/span> are:<\/p>\n<div data-type=\"equation\" id=\"fs-id1167836532368\" class=\"unnumbered\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-926ed8837a52a1fd18b9d88c7a9f42a4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#99;&#99;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#49;&#44;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#50;&#44;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#51;&#44;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#52;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#45;&#49;&#48;&#44;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#45;&#57;&#44;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#45;&#56;&#44;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#45;&#55;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#49;&#53;&#48;&#44;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#49;&#53;&#49;&#44;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#49;&#53;&#50;&#44;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#49;&#53;&#51;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"60\" width=\"223\" style=\"vertical-align: -26px;\" \/><\/div>\n<p id=\"fs-id1167836798146\">Notice that each number is one more than the number preceding it. Therefore, if we define the first integer as <em data-effect=\"italics\">n<\/em>, the next consecutive integer is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-5c36cd99fd08ed06099c3688c7858942_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#43;&#49;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"45\" style=\"vertical-align: -2px;\" \/> The one after that is one more than <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-10312f58cca0b9843be9b54a4569f204_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#43;&#49;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"45\" style=\"vertical-align: -4px;\" \/> so it is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-eca156d5cc03866b25c53029236b77dc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#43;&#49;&#43;&#49;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"76\" style=\"vertical-align: -4px;\" \/> which is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-38b9c5b95101c63c26fd0514f996560c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#43;&#50;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"45\" style=\"vertical-align: -2px;\" \/><\/p>\n<div data-type=\"equation\" id=\"fs-id1167836319415\" class=\"unnumbered\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-5b2f4def73f33ffca610cd34773eab83_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#125;&#110;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#52;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#116;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#105;&#110;&#116;&#101;&#103;&#101;&#114;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#110;&#43;&#49;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#52;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#50;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#110;&#100;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#99;&#111;&#110;&#115;&#101;&#99;&#117;&#116;&#105;&#118;&#101;&#32;&#105;&#110;&#116;&#101;&#103;&#101;&#114;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#110;&#43;&#50;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#52;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#51;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#114;&#100;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#99;&#111;&#110;&#115;&#101;&#99;&#117;&#116;&#105;&#118;&#101;&#32;&#105;&#110;&#116;&#101;&#103;&#101;&#114;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#49;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#101;&#116;&#99;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"62\" width=\"383\" style=\"vertical-align: -25px;\" \/><\/div>\n<p id=\"fs-id1166401599563\">We will use this notation to represent consecutive integers in the next example.<\/p>\n<div data-type=\"example\" id=\"fs-id1167836390345\" class=\"textbox textbox--examples\">\n<div data-type=\"exercise\" id=\"fs-id1167836408144\">\n<div data-type=\"problem\" id=\"fs-id1167836310249\">\n<p id=\"fs-id1167836313850\">Find three consecutive integers whose sum is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-388e2a61e42d29e017c13ab7d3efd660_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;&#52;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"35\" style=\"vertical-align: -1px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\">\n<table id=\"fs-id1167836327805\" class=\"unnumbered unstyled\" summary=\"Step 1 is to read the problem. Step 2 is to identify what we are looking for. They are three consecutive numbers. Step 3 is to name each of the three numbers. Let n be the first integer, n plus 1 the second consecutive integer, and n plus 2 the third consecutive integer. Step 4 is to translate. Restate as one sentence. The sum of the three integers is negative 54. Translate into an equation. The equation is n plus the quantity n plus 1 plus the quantity n plus 2 is equal to negative 54. Step 5 is to solve the equation. Combine like terms. The result is 3 n plus 3 is equal to negative 54. Subtract 3 from each side. The result is 3 n is equal to negative 57. Divide each side by 3. The result is n is equal to negative 19, which is the first integer. The expression n plus 1 is the second integer. Negative 19 plus 1 is negative 18. The expression n plus 2 is the third integer. Negative 19 plus 2 is negative 17. Step 6 is to check. Is negative 19 plus negative 18 plus negative 17 equal to 54? Negative 54 is equal to negative 54. The solutions check. Step 7 is to answer the question. The three consecutive integers are negative 17, negative 18, and negative 19.\" data-label=\"\">\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 1. Read<\/strong> the problem.<\/td>\n<td><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 2. Identify<\/strong> what you are looking for.<\/td>\n<td data-valign=\"top\" data-align=\"left\">three consecutive integers<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 3. Name<\/strong> each of the three numbers<\/td>\n<td data-valign=\"top\" data-align=\"left\">Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-b734576de3bec67d4cc5191e0e847674_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#61;&#123;&#49;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#116;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"53\" style=\"vertical-align: -1px;\" \/> integer.<\/p>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-b656eb41251d3da4308306a98f49a3e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#43;&#49;&#61;&#123;&#50;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#110;&#100;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"90\" style=\"vertical-align: -2px;\" \/> consecutive integer<\/p>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-a7ab37ab531ac382f1c6a08e5204d4c2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#43;&#50;&#61;&#123;&#51;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#114;&#100;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"87\" style=\"vertical-align: -2px;\" \/> consecutive integer<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 4. Translate.<\/strong><\/p>\n<div data-type=\"newline\"><\/div>\n<p>Restate as one sentence.<\/p>\n<div data-type=\"newline\"><\/div>\n<p>Translate into an equation.<\/td>\n<td data-valign=\"top\" data-align=\"left\">\n<div data-type=\"newline\"><\/div>\n<p>The sum of the three integers is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-388e2a61e42d29e017c13ab7d3efd660_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;&#52;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"35\" style=\"vertical-align: -1px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167836283273\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_004a_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 5. Solve<\/strong> the equation.<\/p>\n<div data-type=\"newline\"><\/div>\n<p>Combine like terms.<\/p>\n<div data-type=\"newline\"><\/div>\n<p>Subtract three from each side.<\/p>\n<div data-type=\"newline\"><\/div>\n<p>Divide each side by three.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836511411\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_004b_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167833271911\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_004c_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_004d_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167836585175\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_004e_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167829590326\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_004f_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167836323283\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_004g_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167829721234\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_004h_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167829644849\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_004i_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167833019610\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_004j_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span data-type=\"media\" id=\"fs-id1167833379868\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_004k_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 6. Check.<\/strong><\/p>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-2cd55575e2605b23105e77a9cb3584a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#125;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#45;&#49;&#57;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#45;&#53;&#52;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#45;&#53;&#52;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#45;&#53;&#52;&#10003;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"125\" width=\"150\" style=\"vertical-align: -67px;\" \/><\/td>\n<td><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><strong data-effect=\"bold\">Step 7. Answer<\/strong> the question.<\/td>\n<td data-valign=\"top\" data-align=\"left\">The three consecutive integers are<\/p>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-6b14e0bf4cc6fa4879cf95ca59192a5c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#55;&#44;&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#56;&#44;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"60\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-c10cadbbc56720c2d91a7a0a5f0e1c52_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#57;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"35\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167836613008\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167833381624\">\n<div data-type=\"problem\" id=\"fs-id1167836418736\">\n<p id=\"fs-id1167836340296\">Find three consecutive integers whose sum is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-79590a0d6b9e5427085dd069c567eb42_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#57;&#54;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"35\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836613406\">\n<p id=\"fs-id1167836390229\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-fc7dd560e2c776aa26b7a15ca8599dc3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#51;&#44;&#45;&#51;&#50;&#44;&#45;&#51;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"109\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167836512861\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167829830056\">\n<div data-type=\"problem\" id=\"fs-id1167836552413\">\n<p id=\"fs-id1167836493421\">Find three consecutive integers whose sum is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-adf49d65e3ab43e0bd2c66ac81152c75_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#54;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"35\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836729948\">\n<p id=\"fs-id1167836510061\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-28662bf55d27b9f72d89bcc54ae6b82c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#51;&#44;&#45;&#49;&#50;&#44;&#45;&#49;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"109\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1167836481192\">Now that we have worked with consecutive integers, we will expand our work to include <span data-type=\"term\">consecutive even integers<\/span> and <span data-type=\"term\">consecutive odd integers<\/span>. Consecutive even integers are even integers that immediately follow one another. Examples of consecutive even integers are:<\/p>\n<div data-type=\"equation\" id=\"fs-id1167836320620\" class=\"unnumbered\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-7961dfe2096a8fe41a9478ced9354dd4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#52;&#44;&#32;&#50;&#54;&#44;&#32;&#50;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"75\" style=\"vertical-align: -3px;\" \/><\/div>\n<div data-type=\"equation\" id=\"fs-id1167836320621\" class=\"unnumbered\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-ee5016dcc99f2fbd3ceb8c104b89c400_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#50;&#44;&#45;&#49;&#48;&#44;&#45;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"101\" style=\"vertical-align: -4px;\" \/><\/div>\n<p id=\"fs-id1167829627793\">Notice each integer is two more than the number preceding it. If we call the first one <em data-effect=\"italics\">n<\/em>, then the next one is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-38b9c5b95101c63c26fd0514f996560c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#43;&#50;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"45\" style=\"vertical-align: -2px;\" \/> The one after that would be <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-70d627a93bcc7ae846b0a30b572670a3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#43;&#50;&#43;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"71\" style=\"vertical-align: -2px;\" \/> or <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-3f292a0ae96f7eace85ab1762d557056_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#43;&#52;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"45\" style=\"vertical-align: -2px;\" \/><\/p>\n<div data-type=\"equation\" id=\"fs-id1167836392432\" class=\"unnumbered\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-89b0dd564ca5b3db6b2cc563c2070ba0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#125;&#110;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#52;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#116;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#101;&#118;&#101;&#110;&#32;&#105;&#110;&#116;&#101;&#103;&#101;&#114;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#110;&#43;&#50;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#52;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#50;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#110;&#100;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#99;&#111;&#110;&#115;&#101;&#99;&#117;&#116;&#105;&#118;&#101;&#32;&#101;&#118;&#101;&#110;&#32;&#105;&#110;&#116;&#101;&#103;&#101;&#114;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#110;&#43;&#52;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#52;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#51;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#114;&#100;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#99;&#111;&#110;&#115;&#101;&#99;&#117;&#116;&#105;&#118;&#101;&#32;&#101;&#118;&#101;&#110;&#32;&#105;&#110;&#116;&#101;&#103;&#101;&#114;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#49;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#101;&#116;&#99;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"62\" width=\"424\" style=\"vertical-align: -25px;\" \/><\/div>\n<p id=\"fs-id1167836622525\">Consecutive odd integers are odd integers that immediately follow one another. Consider the consecutive odd integers 63, 65, and 67.<\/p>\n<div data-type=\"equation\" id=\"fs-id1167836527062\" class=\"unnumbered\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-aa9c5717b844e2af7304abdd4b7fc8a4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#54;&#51;&#44;&#32;&#54;&#53;&#44;&#32;&#54;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"75\" style=\"vertical-align: -3px;\" \/><\/div>\n<div data-type=\"equation\" id=\"fs-id1167836527063\" class=\"unnumbered\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-03b0afa120b4e29e18c6d8f59193fee2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#44;&#110;&#43;&#50;&#44;&#110;&#43;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"109\" style=\"vertical-align: -4px;\" \/><\/div>\n<div data-type=\"equation\" id=\"fs-id1167830012042\" class=\"unnumbered\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-40167175b4635afa90779ccfb3f2fc8c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#125;&#110;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#52;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#116;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#111;&#100;&#100;&#32;&#105;&#110;&#116;&#101;&#103;&#101;&#114;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#110;&#43;&#50;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#52;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#50;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#110;&#100;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#99;&#111;&#110;&#115;&#101;&#99;&#117;&#116;&#105;&#118;&#101;&#32;&#111;&#100;&#100;&#32;&#105;&#110;&#116;&#101;&#103;&#101;&#114;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#110;&#43;&#52;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#52;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#51;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#114;&#100;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#99;&#111;&#110;&#115;&#101;&#99;&#117;&#116;&#105;&#118;&#101;&#32;&#111;&#100;&#100;&#32;&#105;&#110;&#116;&#101;&#103;&#101;&#114;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#49;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#101;&#116;&#99;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"62\" width=\"418\" style=\"vertical-align: -25px;\" \/><\/div>\n<p id=\"fs-id1167836434446\">Does it seem strange to have to add two (an even number) to get the next odd number? Do we get an odd number or an even number when we add 2 to 3? to 11? to 47?<\/p>\n<p id=\"fs-id1167829906181\">Whether the problem asks for consecutive even numbers or odd numbers, you do not have to do anything different. The pattern is still the same\u2014to get to the next odd or the next even integer, add two.<\/p>\n<div data-type=\"example\" id=\"fs-id1167836296968\" class=\"textbox textbox--examples\">\n<div data-type=\"exercise\" id=\"fs-id1167836285856\">\n<div data-type=\"problem\" id=\"fs-id1167829691674\">\n<p id=\"fs-id1167836299489\">Find three consecutive even integers whose sum is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-454fa4f8a22c90ab5a5245afd540f8f8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"26\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836550296\">\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-9833fa0501c46d899aa6806a481203c3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#52;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#125;&#92;&#109;&#97;&#116;&#104;&#98;&#102;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#83;&#116;&#101;&#112;&#32;&#49;&#46;&#32;&#82;&#101;&#97;&#100;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#116;&#104;&#101;&#32;&#112;&#114;&#111;&#98;&#108;&#101;&#109;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#92;&#32;&#92;&#109;&#97;&#116;&#104;&#98;&#102;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#83;&#116;&#101;&#112;&#32;&#50;&#46;&#32;&#73;&#100;&#101;&#110;&#116;&#105;&#102;&#121;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#97;&#116;&#32;&#121;&#111;&#117;&#32;&#97;&#114;&#101;&#32;&#108;&#111;&#111;&#107;&#105;&#110;&#103;&#32;&#102;&#111;&#114;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#116;&#104;&#114;&#101;&#101;&#32;&#99;&#111;&#110;&#115;&#101;&#99;&#117;&#116;&#105;&#118;&#101;&#32;&#101;&#118;&#101;&#110;&#32;&#105;&#110;&#116;&#101;&#103;&#101;&#114;&#115;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#109;&#97;&#116;&#104;&#98;&#102;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#83;&#116;&#101;&#112;&#32;&#51;&#46;&#32;&#78;&#97;&#109;&#101;&#46;&#125;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#76;&#101;&#116;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#110;&#61;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#49;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#116;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#101;&#118;&#101;&#110;&#32;&#105;&#110;&#116;&#101;&#103;&#101;&#114;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#38;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#110;&#43;&#50;&#61;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#50;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#110;&#100;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#99;&#111;&#110;&#115;&#101;&#99;&#117;&#116;&#105;&#118;&#101;&#32;&#101;&#118;&#101;&#110;&#32;&#105;&#110;&#116;&#101;&#103;&#101;&#114;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#38;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#110;&#43;&#52;&#61;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#51;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#114;&#100;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#99;&#111;&#110;&#115;&#101;&#99;&#117;&#116;&#105;&#118;&#101;&#32;&#101;&#118;&#101;&#110;&#32;&#105;&#110;&#116;&#101;&#103;&#101;&#114;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#109;&#97;&#116;&#104;&#98;&#102;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#83;&#116;&#101;&#112;&#32;&#52;&#46;&#32;&#84;&#114;&#97;&#110;&#115;&#108;&#97;&#116;&#101;&#46;&#125;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#82;&#101;&#115;&#116;&#97;&#116;&#101;&#32;&#97;&#115;&#32;&#111;&#110;&#101;&#32;&#115;&#101;&#110;&#116;&#101;&#110;&#99;&#101;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#112;&#104;&#97;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title=\"Rendered by QuickLaTeX.com\" height=\"528\" width=\"757\" style=\"vertical-align: -259px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167829741897\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167829741900\">\n<div data-type=\"problem\" id=\"fs-id1167836448166\">\n<p id=\"fs-id1167836448168\">Find three consecutive even integers whose sum is 102.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836318575\">\n<p id=\"fs-id1167836318578\">32, 34, 36<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167833379405\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167833379408\">\n<div data-type=\"problem\" id=\"fs-id1167833379410\">\n<p id=\"fs-id1167836387417\">Find three consecutive even integers whose sum is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-cafc46760bd6e1503473c7f740e9fd5f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#52;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"35\" style=\"vertical-align: -1px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836320083\">\n<p id=\"fs-id1167836320085\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-6b696c1489b3ae94ea305a5549d03332_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#48;&#44;&#45;&#56;&#44;&#45;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"92\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1167836606845\">When a number problem is in a real life context, we still use the same strategies that we used for the previous examples.<\/p>\n<div data-type=\"example\" id=\"fs-id1167836606849\" class=\"textbox textbox--examples\">\n<div data-type=\"exercise\" id=\"fs-id1167829695606\">\n<div data-type=\"problem\" id=\"fs-id1167829695609\">\n<p id=\"fs-id1167829695611\">A married couple together earns ?110,000 a year. The wife earns ?16,000 less than twice what her husband earns. What does the husband earn?<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167829751395\">\n<p id=\"fs-id1167829714064\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-88ba714037fbbcb870f6ae1e66846495_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#99;&#99;&#125;&#92;&#109;&#97;&#116;&#104;&#98;&#102;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#83;&#116;&#101;&#112;&#32;&#49;&#46;&#32;&#82;&#101;&#97;&#100;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#116;&#104;&#101;&#32;&#112;&#114;&#111;&#98;&#108;&#101;&#109;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#92;&#32;&#92;&#109;&#97;&#116;&#104;&#98;&#102;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#83;&#116;&#101;&#112;&#32;&#50;&#46;&#32;&#73;&#100;&#101;&#110;&#116;&#105;&#102;&#121;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#97;&#116;&#32;&#121;&#111;&#117;&#32;&#97;&#114;&#101;&#32;&#108;&#111;&#111;&#107;&#105;&#110;&#103;&#32;&#102;&#111;&#114;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#72;&#111;&#119;&#32;&#109;&#117;&#99;&#104;&#32;&#100;&#111;&#101;&#115;&#32;&#116;&#104;&#101;&#32;&#104;&#117;&#115;&#98;&#97;&#110;&#100;&#32;&#101;&#97;&#114;&#110;&#63;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#109;&#97;&#116;&#104;&#98;&#102;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#83;&#116;&#101;&#112;&#32;&#51;&#46;&#32;&#78;&#97;&#109;&#101;&#46;&#125;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#104;&#111;&#111;&#115;&#101;&#32;&#97;&#32;&#118;&#97;&#114;&#105;&#97;&#98;&#108;&#101;&#32;&#116;&#111;&#32;&#114;&#101;&#112;&#114;&#101;&#115;&#101;&#110;&#116;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#76;&#101;&#116;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#104;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#116;&#104;&#101;&#32;&#97;&#109;&#111;&#117;&#110;&#116;&#32;&#116;&#104;&#101;&#32;&#104;&#117;&#115;&#98;&#97;&#110;&#100;&#32;&#101;&#97;&#114;&#110;&#115;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#116;&#104;&#101;&#32;&#97;&#109;&#111;&#117;&#110;&#116;&#32;&#116;&#104;&#101;&#32;&#104;&#117;&#115;&#98;&#97;&#110;&#100;&#32;&#101;&#97;&#114;&#110;&#115;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#84;&#104;&#101;&#32;&#119;&#105;&#102;&#101;&#32;&#101;&#97;&#114;&#110;&#115;&#32;&#63;&#49;&#54;&#44;&#48;&#48;&#48;&#32;&#108;&#101;&#115;&#115;&#32;&#116;&#104;&#97;&#110;&#32;&#116;&#119;&#105;&#99;&#101;&#32;&#116;&#104;&#97;&#116;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#92;&#32;&#92;&#109;&#97;&#116;&#104;&#98;&#102;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#83;&#116;&#101;&#112;&#32;&#52;&#46;&#32;&#84;&#114;&#97;&#110;&#115;&#108;&#97;&#116;&#101;&#46;&#125;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#92;&#32;&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#82;&#101;&#115;&#116;&#97;&#116;&#101;&#32;&#116;&#104;&#101;&#32;&#112;&#114;&#111;&#98;&#108;&#101;&#109;&#32;&#105;&#110;&#32;&#111;&#110;&#101;&#32;&#115;&#101;&#110;&#116;&#101;&#110;&#99;&#101;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#105;&#116;&#104;&#32;&#97;&#108;&#108;&#32;&#116;&#104;&#101;&#32;&#105;&#109;&#112;&#111;&#114;&#116;&#97;&#110;&#116;&#32;&#105;&#110;&#102;&#111;&#114;&#109;&#97;&#116;&#105;&#111;&#110;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#84;&#114;&#97;&#110;&#115;&#108;&#97;&#116;&#101;&#32;&#105;&#110;&#116;&#111;&#32;&#97;&#110;&#32;&#101;&#113;&#117;&#97;&#116;&#105;&#111;&#110;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#50;&#104;&#45;&#49;&#54;&#44;&#48;&#48;&#48;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#116;&#104;&#101;&#32;&#97;&#109;&#111;&#117;&#110;&#116;&#32;&#116;&#104;&#101;&#32;&#119;&#105;&#102;&#101;&#32;&#101;&#97;&#114;&#110;&#115;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#84;&#111;&#103;&#101;&#116;&#104;&#101;&#114;&#32;&#116;&#104;&#101;&#32;&#104;&#117;&#115;&#98;&#97;&#110;&#100;&#32;&#97;&#110;&#100;&#32;&#119;&#105;&#102;&#101;&#32;&#101;&#97;&#114;&#110;&#32;&#63;&#49;&#49;&#48;&#44;&#48;&#48;&#48;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#104;&#43;&#50;&#104;&#45;&#49;&#54;&#44;&#48;&#48;&#48;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#49;&#49;&#48;&#44;&#48;&#48;&#48;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#92;&#109;&#97;&#116;&#104;&#98;&#102;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#83;&#116;&#101;&#112;&#32;&#53;&#46;&#32;&#83;&#111;&#108;&#118;&#101;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#116;&#104;&#101;&#32;&#101;&#113;&#117;&#97;&#116;&#105;&#111;&#110;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#111;&#109;&#98;&#105;&#110;&#101;&#32;&#108;&#105;&#107;&#101;&#32;&#116;&#101;&#114;&#109;&#115;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#65;&#100;&#100;&#32;&#49;&#54;&#44;&#48;&#48;&#48;&#32;&#116;&#111;&#32;&#98;&#111;&#116;&#104;&#32;&#115;&#105;&#100;&#101;&#115;&#32;&#97;&#110;&#100;&#32;&#115;&#105;&#109;&#112;&#108;&#105;&#102;&#121;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#68;&#105;&#118;&#105;&#100;&#101;&#32;&#101;&#97;&#99;&#104;&#32;&#115;&#105;&#100;&#101;&#32;&#98;&#121;&#32;&#116;&#104;&#114;&#101;&#101;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#104;&#43;&#50;&#104;&#45;&#49;&#54;&#44;&#48;&#48;&#48;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#49;&#49;&#48;&#44;&#48;&#48;&#48;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#51;&#104;&#45;&#49;&#54;&#44;&#48;&#48;&#48;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#49;&#49;&#48;&#44;&#48;&#48;&#48;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#51;&#104;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#49;&#50;&#54;&#44;&#48;&#48;&#48;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#104;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#52;&#50;&#44;&#48;&#48;&#48;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#63;&#52;&#50;&#44;&#48;&#48;&#48;&#32;&#97;&#109;&#111;&#117;&#110;&#116;&#32;&#104;&#117;&#115;&#98;&#97;&#110;&#100;&#32;&#101;&#97;&#114;&#110;&#115;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#92;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#50;&#104;&#45;&#49;&#54;&#44;&#48;&#48;&#48;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#109;&#111;&#117;&#110;&#116;&#32;&#119;&#105;&#102;&#101;&#32;&#101;&#97;&#114;&#110;&#115;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#50;&#44;&#48;&#48;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#49;&#54;&#44;&#48;&#48;&#48;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#56;&#52;&#44;&#48;&#48;&#48;&#45;&#49;&#54;&#44;&#48;&#48;&#48;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#54;&#56;&#44;&#48;&#48;&#48;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#109;&#97;&#116;&#104;&#98;&#102;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#83;&#116;&#101;&#112;&#32;&#54;&#46;&#32;&#67;&#104;&#101;&#99;&#107;&#58;&#125;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#73;&#102;&#32;&#116;&#104;&#101;&#32;&#119;&#105;&#102;&#101;&#32;&#101;&#97;&#114;&#110;&#115;&#32;&#63;&#54;&#56;&#44;&#48;&#48;&#48;&#32;&#97;&#110;&#100;&#32;&#116;&#104;&#101;&#32;&#104;&#117;&#115;&#98;&#97;&#110;&#100;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#101;&#97;&#114;&#110;&#115;&#32;&#63;&#52;&#50;&#44;&#48;&#48;&#48;&#44;&#32;&#105;&#115;&#32;&#116;&#104;&#97;&#116;&#32;&#63;&#49;&#49;&#48;&#44;&#48;&#48;&#48;&#63;&#32;&#89;&#101;&#115;&#33;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#92;&#32;&#92;&#109;&#97;&#116;&#104;&#98;&#102;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#83;&#116;&#101;&#112;&#32;&#55;&#46;&#32;&#65;&#110;&#115;&#119;&#101;&#114;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#116;&#104;&#101;&#32;&#113;&#117;&#101;&#115;&#116;&#105;&#111;&#110;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#84;&#104;&#101;&#32;&#104;&#117;&#115;&#98;&#97;&#110;&#100;&#32;&#101;&#97;&#114;&#110;&#115;&#32;&#63;&#52;&#50;&#44;&#48;&#48;&#48;&#32;&#97;&#32;&#121;&#101;&#97;&#114;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"566\" width=\"787\" style=\"vertical-align: -278px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167836579227\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167836579231\">\n<div data-type=\"problem\" id=\"fs-id1167836579233\">\n<p id=\"fs-id1167836352441\">According to the National Automobile Dealers Association, the average cost of a car in 2014 was ?28,400. This was ?1,600 less than six times the cost in 1975. What was the average cost of a car in 1975?<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836352447\">\n<p id=\"fs-id1167833019123\">The average cost was ?5,000.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167833019129\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167836620867\">\n<div data-type=\"problem\" id=\"fs-id1167836620869\">\n<p id=\"fs-id1167836620872\">US Census data shows that the median price of new home in the U.S. in November 2014 was ?280,900. This was ?10,700 more than 14 times the price in November 1964. What was the median price of a new home in November 1964?<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836513568\">\n<p id=\"fs-id1167836513570\">The median price was ?19,300.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"bc-section section\" data-depth=\"1\" id=\"fs-id1167829683894\">\n<h3 data-type=\"title\">Solve Percent Applications<\/h3>\n<p id=\"fs-id1167829788846\">There are several methods to solve percent equations. In algebra, it is easiest if we just translate English sentences into algebraic equations and then solve the equations. Be sure to change the given percent to a decimal before you use it in the equation.<\/p>\n<div data-type=\"example\" id=\"fs-id1167829788852\" class=\"textbox textbox--examples\">\n<div data-type=\"exercise\" id=\"fs-id1167836300542\">\n<div data-type=\"problem\" id=\"fs-id1167836300544\">\n<p id=\"fs-id1167836300546\">Translate and solve:<\/p>\n<p id=\"fs-id1167836300549\"><span class=\"token\">\u24d0<\/span> What number is 45% of 84?<\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span> 8.5% of what amount is ?4.76?<\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d2<\/span> 168 is what percent of 112?<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836616212\">\n<p id=\"fs-id1167836616214\"><span class=\"token\">\u24d0<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<table id=\"fs-id1167833052126\" class=\"unnumbered unstyled\" summary=\"What number is 45% of 84? Translate into algebra. Let n be the number. Write is 45 percent of 84 as is equal to 0.45 times 84. Multiply. The result is n is equal 37.8. 37.8 is 45 percent of 84.\" data-label=\"\">\n<tbody>\n<tr valign=\"top\">\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167829807494\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_005a_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Translate into algebra. Let <em data-effect=\"italics\">n<\/em> <strong data-effect=\"bold\">=<\/strong> the number.<\/td>\n<td><\/td>\n<td><\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836492976\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_005b_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Multiply.<\/td>\n<td><\/td>\n<td><\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167829594470\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_005c_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td data-valign=\"top\" data-align=\"left\">37.8 is 45% of 84.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div data-type=\"newline\"><\/div>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<table id=\"fs-id1167829614288\" class=\"unnumbered unstyled\" summary=\"What number is 45% of 84? Translate into algebra. Let n be the number. Write is 45 percent of 84 as is equal to 0.45 times 84. Multiply. The result is n is equal 37.8. 37.8 is 45 percent of 84.\" data-label=\"\">\n<tbody>\n<tr valign=\"top\">\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836530002\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_006a_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Translate. Let <em data-effect=\"italics\">n<\/em> <strong data-effect=\"bold\">=<\/strong> the amount.<\/td>\n<td><\/td>\n<td><\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836545347\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_006b_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Multiply.<\/td>\n<td><\/td>\n<td><\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836375560\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_006c_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Divide both sides by 0.085 and simplify.<\/td>\n<td><\/td>\n<td><\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836699980\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_006d_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td data-valign=\"top\" data-align=\"left\">8.5% of ?56 is ?4.76<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div data-type=\"newline\"><\/div>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d2<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<table id=\"fs-id1167832925252\" class=\"unnumbered unstyled\" summary=\"168 is what percent of 112? We are asked to find the percent, so we must have our final result in percent form. Translate into algebra. Let p be equal to the percent. Write 168 is what percent of 112 as 168 is equal to p times 112. Multiply. The result is 168 is equal to 112 p. Divide both sides by 112 and simplify. The result is 1.5 is equal to p. Convert to a percent. The result is 150 percent is equal to p. 168 is 150 percent of 112.\" data-label=\"\">\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">We are asked to find percent, so we must<\/p>\n<div data-type=\"newline\"><\/div>\n<p>have our result in percent form.<\/td>\n<td><\/td>\n<td><\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836629052\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_007a_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Translate into algebra. Let <em data-effect=\"italics\">p<\/em> = the percent.<\/td>\n<td><\/td>\n<td><\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167833019737\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_007b_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Multiply.<\/td>\n<td><\/td>\n<td><\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167833369020\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_007c_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Divide both sides by 112 and simplify.<\/td>\n<td><\/td>\n<td><\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167829589453\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_007d_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Convert to percent.<\/td>\n<td><\/td>\n<td><\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836704270\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_007e_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td data-valign=\"top\" data-align=\"left\">168 is 150% of 112.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167829739356\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167829739361\">\n<div data-type=\"problem\" id=\"fs-id1167829739363\">\n<p id=\"fs-id1167833350221\">Translate and solve: <span class=\"token\">\u24d0<\/span> What number is 45% of 80? <span class=\"token\">\u24d1<\/span> 7.5% of what amount is ?1.95? <span class=\"token\">\u24d2<\/span> 110 is what percent of 88?<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836487171\">\n<p id=\"fs-id1167836487173\"><span class=\"token\">\u24d0<\/span> 36 <span class=\"token\">\u24d1<\/span> ?26 <span class=\"token\">\u24d2<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-ac99f2588f4574d115fe8f3094337e48_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#53;&#37;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"25\" style=\"vertical-align: -1px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167829719452\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167829719456\">\n<div data-type=\"problem\" id=\"fs-id1167829719458\">\n<p id=\"fs-id1167836375371\">Translate and solve: <span class=\"token\">\u24d0<\/span> What number is 55% of 60? <span class=\"token\">\u24d1<\/span> 8.5% of what amount is ?3.06? <span class=\"token\">\u24d0<\/span> 126 is what percent of 72?<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167832935652\">\n<p id=\"fs-id1167832935654\"><span class=\"token\">\u24d0<\/span> 33 <span class=\"token\">\u24d1<\/span> ?36 <span class=\"token\">\u24d0<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-772d97db1bbfe6cab074d174e2e617cd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#55;&#53;&#37;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"25\" style=\"vertical-align: -1px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1167836366381\">Now that we have a problem solving strategy to refer to, and have practiced solving basic percent equations, we are ready to solve percent applications. Be sure to ask yourself if your final answer makes sense\u2014since many of the applications we will solve involve everyday situations, you can rely on your own experience.<\/p>\n<div data-type=\"example\" id=\"fs-id1167836699133\" class=\"textbox textbox--examples\">\n<div data-type=\"exercise\" id=\"fs-id1167829621049\">\n<div data-type=\"problem\" id=\"fs-id1167829621051\">\n<p id=\"fs-id1167829621053\">The label on Audrey\u2019s yogurt said that one serving provided 12 grams of protein, which is 24% of the recommended daily amount. What is the total recommended daily amount of protein?<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167829811256\">\n<table id=\"fs-id1167829621055\" class=\"unnumbered unstyled\" summary=\"What are you asked to find? What total amount of protein is recommended? Choose a variable to represent it. Let a be equal to the total amount of protein. Write a sentence that gives the information to find it. 12 grams is 24 percent of the total amount. So, 12 grams is 24 percent of a. Translate into an equation. 12 is equal to 0.24 times a. Solve. The result is 50 is equal to a. Check. Does this make sense? Yes, 24 percent is about one-fourth if the total and 12 is about one-fourth of 50. Write a complete sentence to answer the question. The amount of protein that is recommended is 50 grams.\" data-label=\"\">\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">What are you asked to find?<\/td>\n<td data-valign=\"top\" data-align=\"left\">What total amount of protein is recommended?<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Choose a variable to represent it.<\/td>\n<td data-valign=\"top\" data-align=\"left\">Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-6fdf9894e43ac86e8b63ba96c72e7181_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#61;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"27\" style=\"vertical-align: 0px;\" \/> total amount of protein.<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Write a sentence that gives the<\/p>\n<div data-type=\"newline\"><\/div>\n<p>information to find it.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836627596\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_008a_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Translate into an equation.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836616307\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_008b_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Solve.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167833340112\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_008c_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Check: Does this make sense?<\/p>\n<div data-type=\"newline\"><\/div>\n<p>Yes, 24% is about <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-83dc4a903812856a369855508d0b2637_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/> of the total and<\/p>\n<div data-type=\"newline\"><\/div>\n<p>12 is about <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-83dc4a903812856a369855508d0b2637_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/> of 50.<\/td>\n<td><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Write a complete sentence to answer the question.<\/td>\n<td data-valign=\"top\" data-align=\"left\">The amount of protein that is recommended is 50 g.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167836543504\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167836543509\">\n<div data-type=\"problem\" id=\"fs-id1167836543511\">\n<p id=\"fs-id1167832940771\">One serving of wheat square cereal has 7 grams of fiber, which is 28% of the recommended daily amount. What is the total recommended daily amount of fiber?<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167832940776\">\n<p id=\"fs-id1167829687282\">25 grams<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167829687288\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167829720045\">\n<div data-type=\"problem\" id=\"fs-id1167829720047\">\n<p id=\"fs-id1167829720049\">One serving of rice cereal has 190 mg of sodium, which is 8% of the recommended daily amount. What is the total recommended daily amount of sodium?<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167829596261\">\n<p id=\"fs-id1167829596263\">2,375 mg<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1166401450383\">Remember to put the answer in the form requested. In the next example we are looking for the percent.<\/p>\n<div data-type=\"example\" id=\"fs-id1167833023048\" class=\"textbox textbox--examples\">\n<div data-type=\"exercise\" id=\"fs-id1167833023050\">\n<div data-type=\"problem\" id=\"fs-id1167833023053\">\n<p id=\"fs-id1167836558499\">Veronica is planning to make muffins from a mix. The package says each muffin will be 240 calories and 60 calories will be from fat. What percent of the total calories is from fat?<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836558505\">\n<table id=\"fs-id1167829645113\" class=\"unnumbered unstyled\" summary=\"What are you asked to find? What percent of the total calories is fat? Choose a variable to represent it. Let p be equal to the percent of fat. Write a sentence that gives the information to find it. What percent of 240 is 60? The percent is p, of 240 is times 240, and is 60 is equal to 60. Translate the sentence into an equation. The equation is p times 240 is equal to 60. Multiply. The result is 240 p is equal to 60. Divided both sides by 240. The result is p is equal to 0.25. Put it in percent form. The result is p is equal to 25 percent. Check. Does this make sense? Yes, 25 percent is one-fourth. 60 is one-fourth of 240. So 25 percent makes sense. Write a complete sentence to answer the question. Of the total calories in each muffin, 25 percent is fat.\" data-label=\"\">\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">What are you asked to find?<\/td>\n<td data-valign=\"top\" data-align=\"left\">What percent of the total calories is fat?<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Choose a variable to represent it.<\/td>\n<td data-valign=\"top\" data-align=\"left\">Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-159263f1bfd0df93391450a8fb398ebc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;&#61;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"28\" style=\"vertical-align: -4px;\" \/> percent of fat.<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Write a sentence that gives the<\/p>\n<div data-type=\"newline\"><\/div>\n<p>information to find it.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836492107\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_009a_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Translate the sentence into an equation.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167829595197\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_009b_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Multiply.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167829746767\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_009c_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Divide both sides by 240.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836626155\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_009d_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Put in percent form.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167829597278\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_009e_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Check: does this make sense?<\/p>\n<div data-type=\"newline\"><\/div>\n<p>Yes, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-1d8d67690cb52f0d2e6e36e804a055a1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#53;&#37;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: 0px;\" \/> is one-fourth; 60 is one-fourth<\/p>\n<div data-type=\"newline\"><\/div>\n<p>of 240. So, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-1d8d67690cb52f0d2e6e36e804a055a1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#53;&#37;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: 0px;\" \/> makes sense.<\/td>\n<td><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Write a complete sentence to answer the question.<\/td>\n<td data-valign=\"top\" data-align=\"left\">Of the total calories in each muffin, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-1d8d67690cb52f0d2e6e36e804a055a1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#53;&#37;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: 0px;\" \/> is fat.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167833329696\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167833329700\">\n<div data-type=\"problem\" id=\"fs-id1167833329703\">\n<p id=\"fs-id1167836606526\">Mitzi received some gourmet brownies as a gift. The wrapper said each 28% brownie was 480 calories, and had 240 calories of fat. What percent of the total calories in each brownie comes from fat? Round the answer to the nearest whole percent.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836606532\">\n<p id=\"fs-id1167836606534\">50%<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167833361796\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167836510879\">\n<div data-type=\"problem\" id=\"fs-id1167836510882\">\n<p id=\"fs-id1167836510884\">The mix Ricardo plans to use to make brownies says that each brownie will be 190 calories, and 76 calories are from fat. What percent of the total calories are from fat? Round the answer to the nearest whole percent.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167824720319\">\n<p id=\"fs-id1167824720321\">40%<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1167829614416\">It is often important in many fields\u2014business, sciences, pop culture\u2014to talk about how much an amount has increased or decreased over a certain period of time. This increase or decrease is generally expressed as a percent and called the <span data-type=\"term\">percent change<\/span>.<\/p>\n<p id=\"fs-id1167836621821\">To find the percent change, first we find the amount of change, by finding the difference of the new amount and the original amount. Then we find what percent the amount of change is of the original amount.<\/p>\n<div data-type=\"note\" class=\"howto\">\n<div data-type=\"title\">Find percent change.<\/div>\n<ol id=\"fs-id1167833086566\" type=\"1\" class=\"stepwise\">\n<li>Find the amount of change.\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-f855d90eb20f3acbda81ee38037eb1e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#99;&#104;&#97;&#110;&#103;&#101;&#125;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#110;&#101;&#119;&#32;&#97;&#109;&#111;&#117;&#110;&#116;&#125;&#45;&#92;&#116;&#101;&#120;&#116;&#123;&#111;&#114;&#105;&#103;&#105;&#110;&#97;&#108;&#32;&#97;&#109;&#111;&#117;&#110;&#116;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"315\" style=\"vertical-align: -3px;\" \/><\/li>\n<li>Find what percent the amount of change is of the original amount.\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-67babf6998e05258febf51c1f6d078b8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#99;&#104;&#97;&#110;&#103;&#101;&#32;&#105;&#115;&#32;&#119;&#104;&#97;&#116;&#32;&#112;&#101;&#114;&#99;&#101;&#110;&#116;&#32;&#111;&#102;&#32;&#116;&#104;&#101;&#32;&#111;&#114;&#105;&#103;&#105;&#110;&#97;&#108;&#32;&#97;&#109;&#111;&#117;&#110;&#116;&#63;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"365\" style=\"vertical-align: -3px;\" \/><\/li>\n<\/ol>\n<\/div>\n<div data-type=\"example\" id=\"fs-id1167836598830\" class=\"textbox textbox--examples\">\n<div data-type=\"exercise\" id=\"fs-id1167836598832\">\n<div data-type=\"problem\" id=\"fs-id1167829743589\">\n<p id=\"fs-id1167829743591\">Recently, the California governor proposed raising community college fees from ?36 a unit to ?46 a unit. Find the percent change. (Round to the nearest tenth of a percent.)<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167829743597\">\n<table id=\"fs-id1167836535293\" class=\"unnumbered unstyled\" summary=\"Find the amount of change. 46 minus 36 is equal to 10. Find the percent. Change is what percent of the original amount? Let p be equal to the percent. 10 is what percent of 36? Translate into an equation. 10 is equal to p times 36. Simplify. The result is 10 is equal to 36 p. Divide both sides 36. The result is 0.278 is approximately equal to p. Change to percent form. Round to the nearest tenth. 27.8 percent is approximately equal to p. Write a complete sentence to answer the question. The new fees are approximately a 27.8 percent increase over the old fees. Remember to round the division to the nearest thousandth in order to round the percent to the nearest tenth.\" data-label=\"\">\n<tbody>\n<tr>\n<td data-valign=\"top\" data-align=\"left\">Find the amount of change.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-692f7f3961d8c4d62e3c7664139b9525_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#54;&#45;&#51;&#54;&#61;&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"99\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Find the percent.<\/td>\n<td data-valign=\"top\" data-align=\"left\">Change is what percent of the original amount?<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-159263f1bfd0df93391450a8fb398ebc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;&#61;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"28\" style=\"vertical-align: -4px;\" \/> the percent.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167833224693\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_010a_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Translate to an equation.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836409496\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_010b_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Simplify.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836578846\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_010c_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Divide both sides by 36.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167824738972\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_010d_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Change to percent form; round to the<\/p>\n<div data-type=\"newline\"><\/div>\n<p>nearest tenth<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167833338974\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_010e_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Write a complete sentence to answer<\/p>\n<div data-type=\"newline\"><\/div>\n<p>the question.<\/td>\n<td data-valign=\"top\" data-align=\"left\">The new fees are approximately a <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-44975451cbca69a0032354850a401c7b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#55;&#46;&#56;&#37;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"32\" style=\"vertical-align: 0px;\" \/> increase<\/p>\n<div data-type=\"newline\"><\/div>\n<p>over the old fees.<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td colspan=\"2\" data-valign=\"top\" data-align=\"left\">Remember to round the division to the nearest thousandth in order to round the percent to the nearest tenth.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167833350522\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167836321413\">\n<div data-type=\"problem\" id=\"fs-id1167836321415\">\n<p id=\"fs-id1167836321418\">Find the percent change. (Round to the nearest tenth of a percent.) In 2011, the IRS increased the deductible mileage cost to 55.5 cents from 51 cents.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836738088\">\n<p id=\"fs-id1167836738091\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-810520c505fc3e583a4077fcf2bb7471_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#46;&#56;&#37;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"23\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167829693674\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167836693062\">\n<div data-type=\"problem\" id=\"fs-id1167836693064\">\n<p id=\"fs-id1167836693066\">Find the percent change. (Round to the nearest tenth of a percent.) In 1995, the standard bus fare in Chicago was ?1.50. In 2008, the standard bus fare was 2.25.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167833024211\">\n<p id=\"fs-id1167833024214\">50%<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1167826172002\">Applications of discount and mark-up are very common in retail settings.<\/p>\n<p id=\"fs-id1167826172005\">When you buy an item on sale, the original price has been discounted by some dollar amount. The <span data-type=\"term\">discount rate<\/span>, usually given as a percent, is used to determine the amount of the discount. To determine the <span data-type=\"term\">amount of discount<\/span>, we multiply the discount rate by the original price.<\/p>\n<p id=\"fs-id1167836424195\">The price a retailer pays for an item is called the <span data-type=\"term\">original cost<\/span>. The retailer then adds a <span data-type=\"term\">mark-up<\/span> to the original cost to get the <span data-type=\"term\">list price<\/span>, the price he sells the item for. The mark-up is usually calculated as a percent of the original cost. To determine the amount of mark-up, multiply the mark-up rate by the original cost.<\/p>\n<div data-type=\"note\" id=\"fs-id1167829590762\">\n<div data-type=\"title\">Discount<\/div>\n<div data-type=\"equation\" id=\"fs-id1167829590767\" class=\"unnumbered\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-cee33c2c13a6aa61375dc1229fee58b3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#109;&#111;&#117;&#110;&#116;&#32;&#111;&#102;&#32;&#100;&#105;&#115;&#99;&#111;&#117;&#110;&#116;&#125;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#100;&#105;&#115;&#99;&#111;&#117;&#110;&#116;&#32;&#114;&#97;&#116;&#101;&#125;&middot;&#92;&#116;&#101;&#120;&#116;&#123;&#111;&#114;&#105;&#103;&#105;&#110;&#97;&#108;&#32;&#112;&#114;&#105;&#99;&#101;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#97;&#108;&#101;&#32;&#112;&#114;&#105;&#99;&#101;&#125;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#111;&#114;&#105;&#103;&#105;&#110;&#97;&#108;&#32;&#97;&#109;&#111;&#117;&#110;&#116;&#125;&#45;&#92;&#116;&#101;&#120;&#116;&#123;&#100;&#105;&#115;&#99;&#111;&#117;&#110;&#116;&#32;&#112;&#114;&#105;&#99;&#101;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"376\" style=\"vertical-align: -14px;\" \/><\/div>\n<p id=\"fs-id1167833197288\">The sale price should always be less than the original price.<\/p>\n<\/div>\n<div data-type=\"note\">\n<div data-type=\"title\">Mark-up<\/div>\n<div data-type=\"equation\" id=\"fs-id1167836375857\" class=\"unnumbered\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-6c26a7c9236ae52a2cc09e00f76fc92b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#109;&#111;&#117;&#110;&#116;&#32;&#111;&#102;&#32;&#109;&#97;&#114;&#107;&#45;&#117;&#112;&#125;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#109;&#97;&#114;&#107;&#45;&#117;&#112;&#32;&#114;&#97;&#116;&#101;&#125;&middot;&#92;&#116;&#101;&#120;&#116;&#123;&#111;&#114;&#105;&#103;&#105;&#110;&#97;&#108;&#32;&#112;&#114;&#105;&#99;&#101;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#108;&#105;&#115;&#116;&#32;&#112;&#114;&#105;&#99;&#101;&#125;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#111;&#114;&#105;&#103;&#105;&#110;&#97;&#108;&#32;&#99;&#111;&#115;&#116;&#125;&#45;&#92;&#116;&#101;&#120;&#116;&#123;&#109;&#97;&#114;&#107;&#45;&#117;&#112;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"378\" style=\"vertical-align: -14px;\" \/><\/div>\n<p id=\"fs-id1167836692588\">The list price should always be more than the original cost.<\/p>\n<\/div>\n<div data-type=\"example\" id=\"fs-id1167836692592\" class=\"textbox textbox--examples\">\n<div data-type=\"exercise\" id=\"fs-id1167836692594\">\n<div data-type=\"problem\" id=\"fs-id1167829688721\">\n<p id=\"fs-id1167829688723\">Liam\u2019s art gallery bought a painting at an original cost of ?750. Liam marked the price up 40%. Find <span class=\"token\">\u24d0<\/span> the amount of mark-up and <span class=\"token\">\u24d1<\/span> the list price of the painting.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836730607\">\n<p id=\"fs-id1167836615159\"><span class=\"token\">\u24d0<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<div data-type=\"newline\"><\/div>\n<table id=\"fs-id1167836615167\" class=\"unnumbered unstyled\" summary=\"Identify what you are asked to find, and choose a variable to represent it. What is the amount of mark-up? Let m be equal to the amount of mark up. Write a sentence that gives the information to find it. The mark-up is 40 percent of the 750 dollar original cost. Translate into an equation. The mark-up is m, is 40 percent is 0.40, of is multiplication, and the ?750 original cost is 750. The equation is m is equal to 0.40 times 750. Solve the equation. The result is m is equal to 300. Write a complete sentence. The mark-up on the painting was 300 dollars.\" data-label=\"\">\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Identify what you are asked to find, and<\/p>\n<div data-type=\"newline\"><\/div>\n<p>choose a variable to represent it.<\/td>\n<td data-valign=\"top\" data-align=\"left\">What is the amount of mark-up?<\/p>\n<div data-type=\"newline\"><\/div>\n<p>Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-0f5541d857afef6f1c8562acca75ad12_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#61;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"33\" style=\"vertical-align: 0px;\" \/> the amount of mark-up.<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Write a sentence that gives the<\/p>\n<div data-type=\"newline\"><\/div>\n<p>information to find it.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836731579\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_011a_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Translate into an equation.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167829850925\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_011b_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Solve the equation.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836620323\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_011c_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Write a complete sentence.<\/td>\n<td data-valign=\"top\" data-align=\"left\">The mark-up on the painting was ?300.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div data-type=\"newline\"><\/div>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<table id=\"fs-id1167836694316\" class=\"unnumbered unstyled can-break\" summary=\"Identify what you are asked to find, and choose a variable to represent it. What is the list price? Let p be equal to the list price. Write a sentence that gives the information to find it. The list price is original cost plus the mark-up. The list price is p, is original cost is equal to 750, plus is the addition sign, the mark-up is 300. Translate into an equation. The result is p is equal to 750 plus 300. Solve the equation. The result is p is equal to 1050. Check. Is this list price more than the original cost? Is 1050 dollars more than 750 dollars? Yes. Write a complete sentence. The list price of the painting was 1050 dollars.\" data-label=\"\">\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Identify what you are asked to find, and<\/p>\n<div data-type=\"newline\"><\/div>\n<p>choose a variable to represent it.<\/td>\n<td data-valign=\"top\" data-align=\"left\">What is the list price?<\/p>\n<div data-type=\"newline\"><\/div>\n<p>Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-159263f1bfd0df93391450a8fb398ebc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;&#61;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"28\" style=\"vertical-align: -4px;\" \/> the list price.<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Write a sentence that gives the<\/p>\n<div data-type=\"newline\"><\/div>\n<p>information to find it.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167833138766\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_012a_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Translate into an equation.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167829691960\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_012b_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Solve the equation.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167829748378\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_012c_img-1.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Check.<\/td>\n<td data-valign=\"top\" data-align=\"left\">Is the list price more than the original cost?<\/p>\n<div data-type=\"newline\"><\/div>\n<p>Is ?1,050 more than ?750? Yes.<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Write a complete sentence.<\/td>\n<td data-valign=\"top\" data-align=\"left\">The list price of the painting was ?1,050.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167829712477\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167833024116\">\n<div data-type=\"problem\" id=\"fs-id1167833024118\">\n<p id=\"fs-id1167833024120\">Find <span class=\"token\">\u24d0<\/span> the amount of mark-up and <span class=\"token\">\u24d1<\/span> the list price: Jim\u2019s music store bought a guitar at original cost ?1,200. Jim marked the price up 50%.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836573666\">\n<p id=\"fs-id1167836573668\"><span class=\"token\">\u24d0<\/span> ?600 <span class=\"token\">\u24d1<\/span> ?1,800<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167836614575\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167836614579\">\n<div data-type=\"problem\" id=\"fs-id1167836614581\">\n<p id=\"fs-id1167836614583\">Find <span class=\"token\">\u24d0<\/span> the amount of mark-up and <span class=\"token\">\u24d1<\/span> the list price: The Auto Resale Store bought Pablo\u2019s Toyota for ?8,500. They marked the price up 35%.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167833059072\">\n<p id=\"fs-id1167833059074\"><span class=\"token\">\u24d0<\/span> ?2,975 <span class=\"token\">\u24d1<\/span> ?11,475<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"bc-section section\" data-depth=\"1\" id=\"fs-id1167836507859\">\n<h3 data-type=\"title\">Solve Simple Interest Applications<\/h3>\n<p id=\"fs-id1167836507865\">Interest is a part of our daily lives. From the interest earned on our savings to the interest we pay on a car loan or credit card debt, we all have some experience with interest in our lives.<\/p>\n<p id=\"fs-id1167832927562\">The amount of money you initially deposit into a bank is called the <span data-type=\"term\">principal<\/span>, <em data-effect=\"italics\">P<\/em>, and the bank pays you <span data-type=\"term\">interest<\/span>, <em data-effect=\"italics\">I.<\/em> When you take out a loan, you pay interest on the amount you borrow, also called the principal.<\/p>\n<p id=\"fs-id1167836707281\">In either case, the interest is computed as a certain percent of the principal, called the <span data-type=\"term\">rate of interest<\/span>, <em data-effect=\"italics\">r<\/em>. The rate of interest is usually expressed as a percent per year, and is calculated by using the decimal equivalent of the percent. The variable <em data-effect=\"italics\">t<\/em>, (for time) represents the number of years the money is saved or borrowed.<\/p>\n<p id=\"fs-id1167836334286\">Interest is calculated as simple interest or compound interest. Here we will use simple interest.<\/p>\n<div data-type=\"note\" id=\"fs-id1167829753593\">\n<div data-type=\"title\">Simple Interest<\/div>\n<p id=\"fs-id1167829753599\">If an amount of money, <em data-effect=\"italics\">P<\/em>, called the principal, is invested or borrowed for a period of <em data-effect=\"italics\">t<\/em> years at an annual interest rate <em data-effect=\"italics\">r<\/em>, the amount of interest, <em data-effect=\"italics\">I<\/em>, earned or paid is<\/p>\n<div data-type=\"equation\" id=\"fs-id1167836607407\" class=\"unnumbered\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-99c8c929658640badb72313f191fe26a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#99;&#99;&#99;&#99;&#99;&#99;&#99;&#99;&#99;&#125;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#73;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#105;&#110;&#116;&#101;&#114;&#101;&#115;&#116;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#73;&#61;&#80;&#114;&#116;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#114;&#101;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#80;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#112;&#114;&#105;&#110;&#99;&#105;&#112;&#97;&#108;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#114;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#114;&#97;&#116;&#101;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#116;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#116;&#105;&#109;&#101;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"78\" width=\"398\" style=\"vertical-align: -33px;\" \/><\/div>\n<p id=\"fs-id1167829906930\">Interest earned or paid according to this formula is called <span data-type=\"term\">simple interest<\/span>.<\/p>\n<\/div>\n<p id=\"fs-id1167832951047\">The formula we use to calculate interest is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-2c321ffce5bab6091002efc85de494e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#73;&#61;&#80;&#114;&#116;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"65\" style=\"vertical-align: 0px;\" \/> To use the formula we substitute in the values for variables that are given, and then solve for the unknown variable. It may be helpful to organize the information in a chart.<\/p>\n<div data-type=\"example\" id=\"fs-id1167836518198\" class=\"textbox textbox--examples\">\n<div data-type=\"exercise\" id=\"fs-id1167836518201\">\n<div data-type=\"problem\" id=\"fs-id1167836518203\">\n<p id=\"fs-id1167836518205\">Areli invested a principal of ?950 in her bank account that earned simple interest at an interest rate of 3%. How much interest did she earn in five years?<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836545229\">\n<p id=\"fs-id1167836545231\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-40299dbe78b971a749a1fdd78b9565d4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#73;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#63;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#80;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#63;&#125;&#57;&#53;&#48;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#114;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#51;&#37;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#116;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#53;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#121;&#101;&#97;&#114;&#115;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"56\" width=\"95\" style=\"vertical-align: -22px;\" \/><\/p>\n<p id=\"fs-id1167833137580\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-53611e9fec275541f1a2ed22474eeb8b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#73;&#100;&#101;&#110;&#116;&#105;&#102;&#121;&#32;&#119;&#104;&#97;&#116;&#32;&#121;&#111;&#117;&#32;&#97;&#114;&#101;&#32;&#97;&#115;&#107;&#101;&#100;&#32;&#116;&#111;&#32;&#102;&#105;&#110;&#100;&#44;&#32;&#97;&#110;&#100;&#32;&#99;&#104;&#111;&#111;&#115;&#101;&#32;&#97;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#87;&#104;&#97;&#116;&#32;&#105;&#115;&#32;&#116;&#104;&#101;&#32;&#115;&#105;&#109;&#112;&#108;&#101;&#32;&#105;&#110;&#116;&#101;&#114;&#101;&#115;&#116;&#63;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#118;&#97;&#114;&#105;&#97;&#98;&#108;&#101;&#32;&#116;&#111;&#32;&#114;&#101;&#112;&#114;&#101;&#115;&#101;&#110;&#116;&#32;&#105;&#116;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#76;&#101;&#116;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#73;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#105;&#110;&#116;&#101;&#114;&#101;&#115;&#116;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#87;&#114;&#105;&#116;&#101;&#32;&#116;&#104;&#101;&#32;&#102;&#111;&#114;&#109;&#117;&#108;&#97;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#51;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#73;&#61;&#80;&#114;&#116;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#83;&#117;&#98;&#115;&#116;&#105;&#116;&#117;&#116;&#101;&#32;&#105;&#110;&#32;&#116;&#104;&#101;&#32;&#103;&#105;&#118;&#101;&#110;&#32;&#105;&#110;&#102;&#111;&#114;&#109;&#97;&#116;&#105;&#111;&#110;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#51;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#73;&#61;&#92;&#108;&#101;&#102;&#116;&#40;&#57;&#53;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#46;&#48;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#83;&#105;&#109;&#112;&#108;&#105;&#102;&#121;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#51;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#73;&#61;&#49;&#52;&#50;&#46;&#53;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#104;&#101;&#99;&#107;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#73;&#115;&#32;&#63;&#49;&#52;&#50;&#46;&#53;&#48;&#32;&#97;&#32;&#114;&#101;&#97;&#115;&#111;&#110;&#97;&#98;&#108;&#101;&#32;&#97;&#109;&#111;&#117;&#110;&#116;&#32;&#111;&#102;&#32;&#105;&#110;&#116;&#101;&#114;&#101;&#115;&#116;&#32;&#111;&#110;&#32;&#63;&#57;&#53;&#48;&#63;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#89;&#101;&#115;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#87;&#114;&#105;&#116;&#101;&#32;&#97;&#32;&#99;&#111;&#109;&#112;&#108;&#101;&#116;&#101;&#32;&#115;&#101;&#110;&#116;&#101;&#110;&#99;&#101;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#84;&#104;&#101;&#32;&#105;&#110;&#116;&#101;&#114;&#101;&#115;&#116;&#32;&#105;&#115;&#32;&#63;&#49;&#52;&#50;&#46;&#53;&#48;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"192\" width=\"704\" style=\"vertical-align: -91px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167833056117\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167829599078\">\n<div data-type=\"problem\" id=\"fs-id1167829599081\">\n<p id=\"fs-id1167829599083\">Nathaly deposited ?12,500 in her bank account where it will earn 4% simple interest. How much interest will Nathaly earn in five years?<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167829599088\">\n<p id=\"fs-id1167829893879\">He will earn ?2,500.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167829893885\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167836526358\">\n<div data-type=\"problem\" id=\"fs-id1167836526361\">\n<p id=\"fs-id1167836526363\">Susana invested a principal of ?36,000 in her bank account that earned simple interest at an interest rate of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-383647a503b071ff2748ba9b27b3d3d5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#46;&#53;&#37;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: 0px;\" \/> How much interest did she earn in three years?<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167829788278\">\n<p id=\"fs-id1167829859754\">She earned ?7,020.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1167829859760\">There may be times when we know the amount of interest earned on a given principal over a certain length of time, but we do not know the rate.<\/p>\n<div data-type=\"example\" id=\"fs-id1167829790848\" class=\"textbox textbox--examples\">\n<div data-type=\"exercise\" id=\"fs-id1167829790850\">\n<div data-type=\"problem\" id=\"fs-id1167829790852\">\n<p id=\"fs-id1167829790855\">Hang borrowed ?7,500 from her parents to pay her tuition. In five years, she paid them ?1,500 interest in addition to the ?7,500 she borrowed. What was the rate of simple interest?<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836407124\">\n<p id=\"fs-id1167836407127\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-f1e6b71e43b350bba8c9aba991ed452f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#73;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#63;&#125;&#49;&#53;&#48;&#48;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#80;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#63;&#125;&#55;&#53;&#48;&#48;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#114;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#63;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#116;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#53;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#121;&#101;&#97;&#114;&#115;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"82\" width=\"112\" style=\"vertical-align: -36px;\" \/><\/p>\n<p id=\"fs-id1167829627509\">\n<pre class=\"ql-errors\">*** QuickLaTeX cannot compile formula:\n&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#73;&#100;&#101;&#110;&#116;&#105;&#102;&#121;&#32;&#119;&#104;&#97;&#116;&#32;&#121;&#111;&#117;&#32;&#97;&#114;&#101;&#32;&#97;&#115;&#107;&#101;&#100;&#32;&#116;&#111;&#32;&#102;&#105;&#110;&#100;&#44;&#32;&#97;&#110;&#100;&#32;&#99;&#104;&#111;&#111;&#115;&#101;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#87;&#104;&#97;&#116;&#32;&#105;&#115;&#32;&#116;&#104;&#101;&#32;&#114;&#97;&#116;&#101;&#32;&#111;&#102;&#32;&#115;&#105;&#109;&#112;&#108;&#101;&#32;&#105;&#110;&#116;&#101;&#114;&#101;&#115;&#116;&#63;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#32;&#118;&#97;&#114;&#105;&#97;&#98;&#108;&#101;&#32;&#116;&#111;&#32;&#114;&#101;&#112;&#114;&#101;&#115;&#101;&#110;&#116;&#32;&#105;&#116;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#87;&#114;&#105;&#116;&#101;&#32;&#116;&#104;&#101;&#32;&#102;&#111;&#114;&#109;&#117;&#108;&#97;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#83;&#117;&#98;&#115;&#116;&#105;&#116;&#117;&#116;&#101;&#32;&#105;&#110;&#32;&#116;&#104;&#101;&#32;&#103;&#105;&#118;&#101;&#110;&#32;&#105;&#110;&#102;&#111;&#114;&#109;&#97;&#116;&#105;&#111;&#110;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#77;&#117;&#108;&#116;&#105;&#112;&#108;&#121;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#68;&#105;&#118;&#105;&#100;&#101;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#104;&#97;&#110;&#103;&#101;&#32;&#116;&#111;&#32;&#112;&#101;&#114;&#99;&#101;&#110;&#116;&#32;&#102;&#111;&#114;&#109;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#76;&#101;&#116;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#114;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#114;&#97;&#116;&#101;&#32;&#111;&#102;&#32;&#105;&#110;&#116;&#101;&#114;&#101;&#115;&#116;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#73;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#80;&#114;&#116;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#49;&#44;&#53;&#48;&#48;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#55;&#44;&#53;&#48;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#114;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#49;&#44;&#53;&#48;&#48;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#51;&#55;&#44;&#53;&#48;&#48;&#114;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#48;&#46;&#48;&#52;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#114;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#52;&#37;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#114;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#104;&#101;&#99;&#107;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#92;&#32;&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#73;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#80;&#114;&#116;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#49;&#44;&#53;&#48;&#48;&#38;&#32;&#92;&#115;&#116;&#97;&#99;&#107;&#114;&#101;&#108;&#123;&#63;&#125;&#123;&#61;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#55;&#44;&#53;&#48;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#46;&#48;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#49;&#44;&#53;&#48;&#48;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#49;&#44;&#53;&#48;&#48;&#10003;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#87;&#114;&#105;&#116;&#101;&#32;&#97;&#32;&#99;&#111;&#109;&#112;&#108;&#101;&#116;&#101;&#32;&#115;&#101;&#110;&#116;&#101;&#110;&#99;&#101;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#84;&#104;&#101;&#32;&#114;&#97;&#116;&#101;&#32;&#111;&#102;&#32;&#105;&#110;&#116;&#101;&#114;&#101;&#115;&#116;&#32;&#119;&#97;&#115;&#32;&#52;&#37;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\n\n*** Error message:\n&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#32;&#111;&#110;&#32;&#105;&#110;&#112;&#117;&#116;&#32;&#108;&#105;&#110;&#101;&#32;&#57;&#32;&#101;&#110;&#100;&#101;&#100;&#32;&#98;&#121;&#32;&#92;&#101;&#110;&#100;&#123;&#100;&#111;&#99;&#117;&#109;&#101;&#110;&#116;&#125;&#46;\r\n&#108;&#101;&#97;&#100;&#105;&#110;&#103;&#32;&#116;&#101;&#120;&#116;&#58;&#32;&#92;&#101;&#110;&#100;&#123;&#100;&#111;&#99;&#117;&#109;&#101;&#110;&#116;&#125;\r\n&#73;&#109;&#112;&#114;&#111;&#112;&#101;&#114;&#32;&#92;&#112;&#114;&#101;&#118;&#100;&#101;&#112;&#116;&#104;&#46;\r\n&#108;&#101;&#97;&#100;&#105;&#110;&#103;&#32;&#116;&#101;&#120;&#116;&#58;&#32;&#92;&#101;&#110;&#100;&#123;&#100;&#111;&#99;&#117;&#109;&#101;&#110;&#116;&#125;\r\n&#77;&#105;&#115;&#115;&#105;&#110;&#103;&#32;&#36;&#32;&#105;&#110;&#115;&#101;&#114;&#116;&#101;&#100;&#46;\r\n&#108;&#101;&#97;&#100;&#105;&#110;&#103;&#32;&#116;&#101;&#120;&#116;&#58;&#32;&#92;&#101;&#110;&#100;&#123;&#100;&#111;&#99;&#117;&#109;&#101;&#110;&#116;&#125;\r\n&#77;&#105;&#115;&#115;&#105;&#110;&#103;&#32;&#125;&#32;&#105;&#110;&#115;&#101;&#114;&#116;&#101;&#100;&#46;\r\n&#108;&#101;&#97;&#100;&#105;&#110;&#103;&#32;&#116;&#101;&#120;&#116;&#58;&#32;&#92;&#101;&#110;&#100;&#123;&#100;&#111;&#99;&#117;&#109;&#101;&#110;&#116;&#125;\r\n&#77;&#105;&#115;&#115;&#105;&#110;&#103;&#32;&#92;&#99;&#114;&#32;&#105;&#110;&#115;&#101;&#114;&#116;&#101;&#100;&#46;\r\n&#108;&#101;&#97;&#100;&#105;&#110;&#103;&#32;&#116;&#101;&#120;&#116;&#58;&#32;&#92;&#101;&#110;&#100;&#123;&#100;&#111;&#99;&#117;&#109;&#101;&#110;&#116;&#125;\r\n&#77;&#105;&#115;&#115;&#105;&#110;&#103;&#32;&#36;&#32;&#105;&#110;&#115;&#101;&#114;&#116;&#101;&#100;&#46;\r\n&#108;&#101;&#97;&#100;&#105;&#110;&#103;&#32;&#116;&#101;&#120;&#116;&#58;&#32;&#92;&#101;&#110;&#100;&#123;&#100;&#111;&#99;&#117;&#109;&#101;&#110;&#116;&#125;\r\n&#89;&#111;&#117;&#32;&#99;&#97;&#110;&#39;&#116;&#32;&#117;&#115;&#101;&#32;&#96;&#92;&#101;&#110;&#100;&#39;&#32;&#105;&#110;&#32;&#105;&#110;&#116;&#101;&#114;&#110;&#97;&#108;&#32;&#118;&#101;&#114;&#116;&#105;&#99;&#97;&#108;&#32;&#109;&#111;&#100;&#101;&#46;\r\n&#108;&#101;&#97;&#100;&#105;&#110;&#103;&#32;&#116;&#101;&#120;&#116;&#58;&#32;&#92;&#101;&#110;&#100;&#123;&#100;&#111;&#99;&#117;&#109;&#101;&#110;&#116;&#125;\r\n&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#32;&#111;&#110;&#32;&#105;&#110;&#112;&#117;&#116;&#32;&#108;&#105;&#110;&#101;&#32;&#57;&#32;&#101;&#110;&#100;&#101;&#100;&#32;&#98;&#121;&#32;&#92;&#101;&#110;&#100;&#123;&#100;&#111;&#99;&#117;&#109;&#101;&#110;&#116;&#125;&#46;\r\n&#108;&#101;&#97;&#100;&#105;&#110;&#103;&#32;&#116;&#101;&#120;&#116;&#58;&#32;&#92;&#101;&#110;&#100;&#123;&#100;&#111;&#99;&#117;&#109;&#101;&#110;&#116;&#125;\r\n&#77;&#105;&#115;&#115;&#105;&#110;&#103;&#32;&#125;&#32;&#105;&#110;&#115;&#101;&#114;&#116;&#101;&#100;&#46;\r\n&#108;&#101;&#97;&#100;&#105;&#110;&#103;&#32;&#116;&#101;&#120;&#116;&#58;&#32;&#92;&#101;&#110;&#100;&#123;&#100;&#111;&#99;&#117;&#109;&#101;&#110;&#116;&#125;\r\n&#69;&#109;&#101;&#114;&#103;&#101;&#110;&#99;&#121;&#32;&#115;&#116;&#111;&#112;&#46;\r\n\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167836774787\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167836630614\">\n<div data-type=\"problem\" id=\"fs-id1167836630616\">\n<p id=\"fs-id1167836630618\">Jim lent his sister ?5,000 to help her buy a house. In three years, she paid him the ?5,000, plus ?900 interest. What was the rate of simple interest?<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836408266\">\n<p id=\"fs-id1167836408269\">The rate of simple interest was 6%.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167836408275\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167836553008\">\n<div data-type=\"problem\" id=\"fs-id1167836553010\">\n<p id=\"fs-id1167836553012\">Loren lent his brother ?3,000 to help him buy a car. In four years, his brother paid him back the ?3,000 plus ?660 in interest. What was the rate of simple interest?<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167832961256\">\n<p id=\"fs-id1167832961259\">The rate of simple interest was 5.5%.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1167832961265\">In the next example, we are asked to find the principal\u2014the amount borrowed.<\/p>\n<div data-type=\"example\" id=\"fs-id1167836546286\" class=\"textbox textbox--examples\">\n<div data-type=\"exercise\" id=\"fs-id1167836546288\">\n<div data-type=\"problem\" id=\"fs-id1167836546290\">\n<p id=\"fs-id1167836546292\">Sean\u2019s new car loan statement said he would pay ?4,866,25 in interest from a simple interest rate of 8.5% over five years. How much did he borrow to buy his new car?<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167829879766\">\n<p id=\"fs-id1167829879769\">\n<pre class=\"ql-errors\">*** QuickLaTeX cannot compile formula:\n&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#73;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#52;&#44;&#56;&#54;&#54;&#46;&#50;&#53;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#80;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#63;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#114;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#56;&#46;&#53;&#37;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#116;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#53;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#121;&#101;&#97;&#114;&#115;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\n\n*** Error message:\n&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#32;&#111;&#110;&#32;&#105;&#110;&#112;&#117;&#116;&#32;&#108;&#105;&#110;&#101;&#32;&#57;&#32;&#101;&#110;&#100;&#101;&#100;&#32;&#98;&#121;&#32;&#92;&#101;&#110;&#100;&#123;&#100;&#111;&#99;&#117;&#109;&#101;&#110;&#116;&#125;&#46;\r\n&#108;&#101;&#97;&#100;&#105;&#110;&#103;&#32;&#116;&#101;&#120;&#116;&#58;&#32;&#92;&#101;&#110;&#100;&#123;&#100;&#111;&#99;&#117;&#109;&#101;&#110;&#116;&#125;\r\n&#73;&#109;&#112;&#114;&#111;&#112;&#101;&#114;&#32;&#92;&#112;&#114;&#101;&#118;&#100;&#101;&#112;&#116;&#104;&#46;\r\n&#108;&#101;&#97;&#100;&#105;&#110;&#103;&#32;&#116;&#101;&#120;&#116;&#58;&#32;&#92;&#101;&#110;&#100;&#123;&#100;&#111;&#99;&#117;&#109;&#101;&#110;&#116;&#125;\r\n&#77;&#105;&#115;&#115;&#105;&#110;&#103;&#32;&#36;&#32;&#105;&#110;&#115;&#101;&#114;&#116;&#101;&#100;&#46;\r\n&#108;&#101;&#97;&#100;&#105;&#110;&#103;&#32;&#116;&#101;&#120;&#116;&#58;&#32;&#92;&#101;&#110;&#100;&#123;&#100;&#111;&#99;&#117;&#109;&#101;&#110;&#116;&#125;\r\n&#77;&#105;&#115;&#115;&#105;&#110;&#103;&#32;&#125;&#32;&#105;&#110;&#115;&#101;&#114;&#116;&#101;&#100;&#46;\r\n&#108;&#101;&#97;&#100;&#105;&#110;&#103;&#32;&#116;&#101;&#120;&#116;&#58;&#32;&#92;&#101;&#110;&#100;&#123;&#100;&#111;&#99;&#117;&#109;&#101;&#110;&#116;&#125;\r\n&#77;&#105;&#115;&#115;&#105;&#110;&#103;&#32;&#92;&#99;&#114;&#32;&#105;&#110;&#115;&#101;&#114;&#116;&#101;&#100;&#46;\r\n&#108;&#101;&#97;&#100;&#105;&#110;&#103;&#32;&#116;&#101;&#120;&#116;&#58;&#32;&#92;&#101;&#110;&#100;&#123;&#100;&#111;&#99;&#117;&#109;&#101;&#110;&#116;&#125;\r\n&#77;&#105;&#115;&#115;&#105;&#110;&#103;&#32;&#36;&#32;&#105;&#110;&#115;&#101;&#114;&#116;&#101;&#100;&#46;\r\n&#108;&#101;&#97;&#100;&#105;&#110;&#103;&#32;&#116;&#101;&#120;&#116;&#58;&#32;&#92;&#101;&#110;&#100;&#123;&#100;&#111;&#99;&#117;&#109;&#101;&#110;&#116;&#125;\r\n&#89;&#111;&#117;&#32;&#99;&#97;&#110;&#39;&#116;&#32;&#117;&#115;&#101;&#32;&#96;&#92;&#101;&#110;&#100;&#39;&#32;&#105;&#110;&#32;&#105;&#110;&#116;&#101;&#114;&#110;&#97;&#108;&#32;&#118;&#101;&#114;&#116;&#105;&#99;&#97;&#108;&#32;&#109;&#111;&#100;&#101;&#46;\r\n&#108;&#101;&#97;&#100;&#105;&#110;&#103;&#32;&#116;&#101;&#120;&#116;&#58;&#32;&#92;&#101;&#110;&#100;&#123;&#100;&#111;&#99;&#117;&#109;&#101;&#110;&#116;&#125;\r\n&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#32;&#111;&#110;&#32;&#105;&#110;&#112;&#117;&#116;&#32;&#108;&#105;&#110;&#101;&#32;&#57;&#32;&#101;&#110;&#100;&#101;&#100;&#32;&#98;&#121;&#32;&#92;&#101;&#110;&#100;&#123;&#100;&#111;&#99;&#117;&#109;&#101;&#110;&#116;&#125;&#46;\r\n&#108;&#101;&#97;&#100;&#105;&#110;&#103;&#32;&#116;&#101;&#120;&#116;&#58;&#32;&#92;&#101;&#110;&#100;&#123;&#100;&#111;&#99;&#117;&#109;&#101;&#110;&#116;&#125;\r\n&#77;&#105;&#115;&#115;&#105;&#110;&#103;&#32;&#125;&#32;&#105;&#110;&#115;&#101;&#114;&#116;&#101;&#100;&#46;\r\n&#108;&#101;&#97;&#100;&#105;&#110;&#103;&#32;&#116;&#101;&#120;&#116;&#58;&#32;&#92;&#101;&#110;&#100;&#123;&#100;&#111;&#99;&#117;&#109;&#101;&#110;&#116;&#125;\r\n&#69;&#109;&#101;&#114;&#103;&#101;&#110;&#99;&#121;&#32;&#115;&#116;&#111;&#112;&#46;\r\n\n<\/pre>\n<p id=\"fs-id1167836558133\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-1793f4937c54be4b4c5a78f1febfbb94_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#73;&#100;&#101;&#110;&#116;&#105;&#102;&#121;&#32;&#119;&#104;&#97;&#116;&#32;&#121;&#111;&#117;&#32;&#97;&#114;&#101;&#32;&#97;&#115;&#107;&#101;&#100;&#32;&#116;&#111;&#32;&#102;&#105;&#110;&#100;&#44;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#87;&#104;&#97;&#116;&#32;&#105;&#115;&#32;&#116;&#104;&#101;&#32;&#97;&#109;&#111;&#117;&#110;&#116;&#32;&#98;&#111;&#114;&#114;&#111;&#119;&#101;&#100;&#32;&#40;&#116;&#104;&#101;&#32;&#112;&#114;&#105;&#110;&#99;&#105;&#112;&#97;&#108;&#41;&#63;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#110;&#100;&#32;&#99;&#104;&#111;&#111;&#115;&#101;&#32;&#97;&#32;&#118;&#97;&#114;&#105;&#97;&#98;&#108;&#101;&#32;&#116;&#111;&#32;&#114;&#101;&#112;&#114;&#101;&#115;&#101;&#110;&#116;&#32;&#105;&#116;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#87;&#114;&#105;&#116;&#101;&#32;&#116;&#104;&#101;&#32;&#102;&#111;&#114;&#109;&#117;&#108;&#97;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#83;&#117;&#98;&#115;&#116;&#105;&#116;&#117;&#116;&#101;&#32;&#105;&#110;&#32;&#116;&#104;&#101;&#32;&#103;&#105;&#118;&#101;&#110;&#32;&#105;&#110;&#102;&#111;&#114;&#109;&#97;&#116;&#105;&#111;&#110;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#77;&#117;&#108;&#116;&#105;&#112;&#108;&#121;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#68;&#105;&#118;&#105;&#100;&#101;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#76;&#101;&#116;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#80;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#112;&#114;&#105;&#110;&#99;&#105;&#112;&#97;&#108;&#32;&#98;&#111;&#114;&#114;&#111;&#119;&#101;&#100;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#73;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#80;&#114;&#116;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#52;&#44;&#56;&#54;&#54;&#46;&#50;&#53;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#80;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#46;&#48;&#56;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#52;&#44;&#56;&#54;&#54;&#46;&#50;&#53;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#48;&#46;&#52;&#50;&#53;&#80;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#49;&#49;&#44;&#52;&#53;&#48;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#80;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#104;&#101;&#99;&#107;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#92;&#32;&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#73;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#80;&#114;&#116;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#52;&#44;&#56;&#54;&#54;&#46;&#50;&#53;&#38;&#32;&#92;&#115;&#116;&#97;&#99;&#107;&#114;&#101;&#108;&#123;&#63;&#125;&#123;&#61;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#49;&#44;&#52;&#53;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#46;&#48;&#56;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#52;&#44;&#56;&#54;&#54;&#46;&#50;&#53;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#52;&#44;&#56;&#54;&#54;&#46;&#50;&#53;&#10003;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#92;&#32;&#92;&#92;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#87;&#114;&#105;&#116;&#101;&#32;&#97;&#32;&#99;&#111;&#109;&#112;&#108;&#101;&#116;&#101;&#32;&#115;&#101;&#110;&#116;&#101;&#110;&#99;&#101;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#84;&#104;&#101;&#32;&#112;&#114;&#105;&#110;&#99;&#105;&#112;&#97;&#108;&#32;&#119;&#97;&#115;&#32;&#63;&#49;&#49;&#44;&#52;&#53;&#48;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"287\" width=\"723\" style=\"vertical-align: -138px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167836700880\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167836700884\">\n<div data-type=\"problem\" id=\"fs-id1167836518297\">\n<p>Eduardo noticed that his new car loan papers stated that with a 7.5% simple interest rate, he would pay ?6,596.25 in interest over five years. How much did he borrow to pay for his car?<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836518305\">\n<p id=\"fs-id1167836518307\">He paid ?17,590.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167836729457\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167836729461\">\n<div data-type=\"problem\" id=\"fs-id1167836729463\">\n<p id=\"fs-id1167832989118\">In five years, Gloria\u2019s bank account earned ?2,400 interest at 5% simple interest. How much had she deposited in the account?<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167832989125\">\n<p id=\"fs-id1167832989127\">She deposited ?9,600.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167829766743\" class=\"media-2\">\n<p id=\"fs-id1167829766746\">Access this online resource for additional instruction and practice with using a problem solving strategy.<\/p>\n<ul id=\"fs-id1167833056662\" data-display=\"block\">\n<li><a href=\"https:\/\/openstax.org\/l\/37begalgwordpro\">Begining Arithmetic Problems<\/a><\/li>\n<\/ul>\n<\/div>\n<div class=\"textbox\" data-depth=\"1\" id=\"fs-id1167836596031\">\n<h3 data-type=\"title\">Key Concepts<\/h3>\n<ul id=\"fs-id1167836596038\" data-bullet-style=\"bullet\">\n<li><strong data-effect=\"bold\">How To Use a Problem Solving Strategy for Word Problems<\/strong>\n<ol id=\"fs-id1167833224418\" type=\"1\" class=\"stepwise\">\n<li><strong data-effect=\"bold\">Read<\/strong> the problem. Make sure all the words and ideas are understood.<\/li>\n<li><strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/li>\n<li><strong data-effect=\"bold\">Name<\/strong> what you are looking for. Choose a variable to represent that quantity.<\/li>\n<li><strong data-effect=\"bold\">Translate<\/strong> into an equation. It may be helpful to restate the problem in one sentence with all the important information. Then, translate the English sentence into an algebra equation.<\/li>\n<li><strong data-effect=\"bold\">Solve<\/strong> the equation using proper algebra techniques.\n<div data-type=\"newline\"><\/div>\n<p id=\"fs-id1167833051048\">\n<div data-type=\"newline\"><\/div>\n<div data-type=\"newline\"><\/div>\n<\/li>\n<li><strong data-effect=\"bold\">Check<\/strong> the answer in the problem to make sure it makes sense.<\/li>\n<li><strong data-effect=\"bold\">Answer<\/strong> the question with a complete sentence.<\/li>\n<\/ol>\n<\/li>\n<li><strong data-effect=\"bold\">How To Find Percent Change<\/strong>\n<ol type=\"1\" class=\"stepwise\">\n<li>Find the amount of change\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-f855d90eb20f3acbda81ee38037eb1e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#99;&#104;&#97;&#110;&#103;&#101;&#125;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#110;&#101;&#119;&#32;&#97;&#109;&#111;&#117;&#110;&#116;&#125;&#45;&#92;&#116;&#101;&#120;&#116;&#123;&#111;&#114;&#105;&#103;&#105;&#110;&#97;&#108;&#32;&#97;&#109;&#111;&#117;&#110;&#116;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"315\" style=\"vertical-align: -3px;\" \/><\/li>\n<li>Find what percent the amount of change is of the original amount.\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-67babf6998e05258febf51c1f6d078b8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#99;&#104;&#97;&#110;&#103;&#101;&#32;&#105;&#115;&#32;&#119;&#104;&#97;&#116;&#32;&#112;&#101;&#114;&#99;&#101;&#110;&#116;&#32;&#111;&#102;&#32;&#116;&#104;&#101;&#32;&#111;&#114;&#105;&#103;&#105;&#110;&#97;&#108;&#32;&#97;&#109;&#111;&#117;&#110;&#116;&#63;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"365\" style=\"vertical-align: -3px;\" \/><\/li>\n<\/ol>\n<\/li>\n<li><strong data-effect=\"bold\">Discount<\/strong>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-c52e5c8b3e5362b896c451dd6a55bacc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#109;&#111;&#117;&#110;&#116;&#32;&#111;&#102;&#32;&#100;&#105;&#115;&#99;&#111;&#117;&#110;&#116;&#125;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#100;&#105;&#115;&#99;&#111;&#117;&#110;&#116;&#32;&#114;&#97;&#116;&#101;&#125;&middot;&#92;&#116;&#101;&#120;&#116;&#123;&#111;&#114;&#105;&#103;&#105;&#110;&#97;&#108;&#32;&#112;&#114;&#105;&#99;&#101;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#97;&#108;&#101;&#32;&#112;&#114;&#105;&#99;&#101;&#125;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#111;&#114;&#105;&#103;&#105;&#110;&#97;&#108;&#32;&#97;&#109;&#111;&#117;&#110;&#116;&#125;&#45;&#92;&#116;&#101;&#120;&#116;&#123;&#100;&#105;&#115;&#99;&#111;&#117;&#110;&#116;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"60\" width=\"404\" style=\"vertical-align: -25px;\" \/><\/li>\n<li><strong data-effect=\"bold\">Mark-up<\/strong>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-c13b241df7fd1de6b6ad12c66252dc4e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#109;&#111;&#117;&#110;&#116;&#32;&#111;&#102;&#32;&#109;&#97;&#114;&#107;&#45;&#117;&#112;&#125;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#109;&#97;&#114;&#107;&#45;&#117;&#112;&#32;&#114;&#97;&#116;&#101;&#125;&middot;&#92;&#116;&#101;&#120;&#116;&#123;&#111;&#114;&#105;&#103;&#105;&#110;&#97;&#108;&#32;&#99;&#111;&#115;&#116;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#108;&#105;&#115;&#116;&#32;&#112;&#114;&#105;&#99;&#101;&#125;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#111;&#114;&#105;&#103;&#105;&#110;&#97;&#108;&#32;&#99;&#111;&#115;&#116;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#43;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#109;&#97;&#114;&#107;&#32;&#117;&#112;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"60\" width=\"393\" style=\"vertical-align: -25px;\" \/><\/li>\n<li><strong data-effect=\"bold\">Simple Interest<\/strong>\n<div data-type=\"newline\"><\/div>\n<p> If an amount of money, <em data-effect=\"italics\">P<\/em>, called the principal, is invested or borrowed for a period of <em data-effect=\"italics\">t<\/em> years at an annual interest rate <em data-effect=\"italics\">r<\/em>, the amount of interest, <em data-effect=\"italics\">I<\/em>, earned or paid is:<\/p>\n<div data-type=\"newline\"><\/div>\n<div data-type=\"equation\" id=\"fs-id1167835181891\" class=\"unnumbered\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-69fb315aef9a4bc070dce23767635ac2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#99;&#125;&#38;&#32;&#38;&#32;&#73;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#105;&#110;&#116;&#101;&#114;&#101;&#115;&#116;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#73;&#61;&#80;&#114;&#116;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#114;&#101;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#80;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#112;&#114;&#105;&#110;&#99;&#105;&#112;&#97;&#108;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#38;&#32;&#38;&#32;&#114;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#114;&#97;&#116;&#101;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#38;&#32;&#38;&#32;&#116;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#116;&#105;&#109;&#101;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"78\" width=\"304\" style=\"vertical-align: -33px;\" \/><\/div>\n<\/li>\n<\/ul>\n<\/div>\n<div class=\"textbox\" data-depth=\"1\" id=\"fs-id1167836300510\">\n<div class=\"practice-perfect\" data-depth=\"2\" id=\"fs-id1167836300514\">\n<h4 data-type=\"title\">Practice Makes Perfect<\/h4>\n<p id=\"fs-id1167836300522\"><strong data-effect=\"bold\">Use a Problem Solving Strategy for Word Problems<\/strong><\/p>\n<div data-type=\"exercise\" id=\"fs-id1167833340063\">\n<div data-type=\"problem\" id=\"fs-id1167833340065\">\n<p id=\"fs-id1167833340068\">List five positive thoughts you can say to yourself that will help you approach word problems with a positive attitude. You may want to copy them on a sheet of paper and put it in the front of your notebook, where you can read them often.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836538791\">\n<p id=\"fs-id1167836538793\">Answers will vary.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836538799\">\n<div data-type=\"problem\" id=\"fs-id1167829931415\">\n<p id=\"fs-id1167829931417\">List five negative thoughts that you have said to yourself in the past that will hinder your progress on word problems. You may want to write each one on a small piece of paper and rip it up to symbolically destroy the negative thoughts.<\/p>\n<\/div>\n<\/div>\n<p id=\"fs-id1167836605126\">In the following exercises, solve using the problem solving strategy for word problems. Remember to write a complete sentence to answer each question.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167836605131\">\n<div data-type=\"problem\" id=\"fs-id1167836605133\">\n<p id=\"fs-id1167836605135\">There are 16 girls in a school club. The number of girls is four more than twice the number of boys. Find the number of boys.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167833049947\">\n<p id=\"fs-id1167833049949\">six boys<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167833049954\">\n<div data-type=\"problem\" id=\"fs-id1167836649991\">\n<p id=\"fs-id1167836649993\">There are 18 Cub Scouts in Troop 645. The number of scouts is three more than five times the number of adult leaders. Find the number of adult leaders.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167826170306\">\n<div data-type=\"problem\" id=\"fs-id1167826170308\">\n<p id=\"fs-id1167826170310\">Huong is organizing paperback and hardback books for her club\u2019s used book sale. The number of paperbacks is 12 less than three times the number of hardbacks. Huong had 162 paperbacks. How many hardback books were there?<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167826170315\">\n<p id=\"fs-id1167836493523\">58 hardback books<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836493529\">\n<div data-type=\"problem\" id=\"fs-id1167836416628\">\n<p id=\"fs-id1167836416630\">Jeff is lining up children\u2019s and adult bicycles at the bike shop where he works. The number of children\u2019s bicycles is nine less than three times the number of adult bicycles. There are 42 adult bicycles. How many children\u2019s bicycles are there?<\/p>\n<\/div>\n<\/div>\n<p id=\"fs-id1167836624582\"><strong data-effect=\"bold\">Solve Number Word Problems<\/strong><\/p>\n<p id=\"fs-id1167836624588\">In the following exercises, solve each number word problem.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167836688863\">\n<div data-type=\"problem\" id=\"fs-id1167836688865\">\n<p id=\"fs-id1167836688867\">The difference of a number and 12 is three. Find the number.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836688871\">\n<p id=\"fs-id1167836688873\">15<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836321013\">\n<div data-type=\"problem\" id=\"fs-id1167836321015\">\n<p id=\"fs-id1167836321017\">The difference of a number and eight is four. Find the number.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836363696\">\n<div data-type=\"problem\" id=\"fs-id1167836363698\">\n<p id=\"fs-id1167836363701\">The sum of three times a number and eight is 23. Find the number.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167833224664\">\n<p id=\"fs-id1167833224666\">5<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167833224672\">\n<div data-type=\"problem\" id=\"fs-id1167836433966\">\n<p id=\"fs-id1167836433968\">The sum of twice a number and six is 14. Find the number.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829789166\">\n<div data-type=\"problem\" id=\"fs-id1167829789168\">\n<p>The difference of twice a number and seven is 17. Find the number.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167829789174\">\n<p id=\"fs-id1167829789176\">12<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167833047200\">\n<div data-type=\"problem\" id=\"fs-id1167833047202\">\n<p id=\"fs-id1167833047204\">The difference of four times a number and seven is 21. Find the number.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167833328973\">\n<div data-type=\"problem\" id=\"fs-id1167833328975\">\n<p id=\"fs-id1167833328978\">Three times the sum of a number and nine is 12. Find the number.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836697750\">\n<p id=\"fs-id1167836697752\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-7b5b9d9f382b11767d19f257afca0019_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167832940609\">\n<div data-type=\"problem\" id=\"fs-id1167832940611\">\n<p id=\"fs-id1167832940614\">Six times the sum of a number and eight is 30. Find the number.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167832994440\">\n<div data-type=\"problem\" id=\"fs-id1167832994442\">\n<p id=\"fs-id1167832994444\">One number is six more than the other. Their sum is 42. Find the numbers.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167829747774\">\n<p id=\"fs-id1167829747776\">18, 24<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829747782\">\n<div data-type=\"problem\" id=\"fs-id1167833386692\">\n<p id=\"fs-id1167833386694\">One number is five more than the other. Their sum is 33. Find the numbers.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829590410\">\n<div data-type=\"problem\" id=\"fs-id1167829590412\">\n<p id=\"fs-id1167829590414\">The sum of two numbers is 20. One number is four less than the other. Find the numbers.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167829590419\">\n<p id=\"fs-id1167829590421\">8, 12<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829717297\">\n<div data-type=\"problem\" id=\"fs-id1167829717300\">\n<p id=\"fs-id1167829717302\">The sum of two numbers is 27. One number is seven less than the other. Find the numbers.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836732384\">\n<div data-type=\"problem\" id=\"fs-id1167836732386\">\n<p id=\"fs-id1167833311250\">One number is 14 less than another. If their sum is increased by seven, the result is 85. Find the numbers.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167833311255\">\n<p id=\"fs-id1167833311257\">32, 46<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836730384\">\n<div data-type=\"problem\" id=\"fs-id1167836730386\">\n<p id=\"fs-id1167836730388\">One number is 11 less than another. If their sum is increased by eight, the result is 71. Find the numbers.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167824732299\">\n<div data-type=\"problem\" id=\"fs-id1167824732301\">\n<p id=\"fs-id1167824732303\">The sum of two numbers is 14. One number is two less than three times the other. Find the numbers.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836610765\">\n<p id=\"fs-id1167836610767\">4, 10<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836610772\">\n<div data-type=\"problem\" id=\"fs-id1167836610774\">\n<p id=\"fs-id1167829843968\">The sum of two numbers is zero. One number is nine less than twice the other. Find the numbers.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167833274532\">\n<div data-type=\"problem\" id=\"fs-id1167833274534\">\n<p id=\"fs-id1167833274536\">The sum of two consecutive integers is 77. Find the integers.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836610798\">\n<p id=\"fs-id1167836610800\">38, 39<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836610805\">\n<div data-type=\"problem\" id=\"fs-id1167833380167\">\n<p id=\"fs-id1167833380169\">The sum of two consecutive integers is 89. Find the integers.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167826206362\">\n<div data-type=\"problem\" id=\"fs-id1167826206365\">\n<p id=\"fs-id1167826206367\">The sum of three consecutive integers is 78. Find the integers.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167826206371\">\n<p id=\"fs-id1167826206373\">25, 26, 27<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167833071653\">\n<div data-type=\"problem\" id=\"fs-id1167833071655\">\n<p id=\"fs-id1167833071657\">The sum of three consecutive integers is 60. Find the integers.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167833240038\">\n<div data-type=\"problem\" id=\"fs-id1167833240040\">\n<p id=\"fs-id1167833240042\">Find three consecutive integers whose sum is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-adf49d65e3ab43e0bd2c66ac81152c75_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#54;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"35\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\">\n<p id=\"fs-id1167836546323\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-78979a60c1272f7a604af5fe7a1a5abf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#49;&#44;&#45;&#49;&#50;&#44;&#45;&#49;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"110\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836507071\">\n<div data-type=\"problem\" id=\"fs-id1167836507073\">\n<p id=\"fs-id1167836507075\">Find three consecutive integers whose sum is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-cfa36400e576c82fd4847d2da37b1d56_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"26\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836448552\">\n<div data-type=\"problem\" id=\"fs-id1167836508931\">\n<p id=\"fs-id1167836508933\">Find three consecutive even integers whose sum is 258.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836508938\">\n<p id=\"fs-id1167836508940\">84, 86, 88<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836415038\">\n<div data-type=\"problem\" id=\"fs-id1167836415040\">\n<p id=\"fs-id1167836415042\">Find three consecutive even integers whose sum is 222.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836514322\">\n<div data-type=\"problem\" id=\"fs-id1167836514324\">\n<p id=\"fs-id1167836514326\">Find three consecutive odd integers whose sum is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-168f5a9199434437de951555558f0e9c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#49;&#51;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"44\" style=\"vertical-align: -1px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836408908\">\n<p id=\"fs-id1167836408910\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-6b46cade56ae903904bd872fda1b0ca7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#54;&#57;&#44;&#45;&#55;&#49;&#44;&#45;&#55;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"110\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836513517\">\n<div data-type=\"problem\" id=\"fs-id1167836513519\">\n<p id=\"fs-id1167836513521\">Find three consecutive odd integers whose sum is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-f5327833426ff5b8c55213c5d9ef5d2f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#54;&#55;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"44\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167833397290\">\n<div data-type=\"problem\" id=\"fs-id1167833397292\">\n<p id=\"fs-id1167836492064\">Philip pays ?1,620 in rent every month. This amount is ?120 more than twice what his brother Paul pays for rent. How much does Paul pay for rent?<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836492069\">\n<p id=\"fs-id1167836492072\">?750<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829853727\">\n<div data-type=\"problem\" id=\"fs-id1167829853729\">\n<p id=\"fs-id1167829853731\">Marc just bought an SUV for ?54,000. This is ?7,400 less than twice what his wife paid for her car last year. How much did his wife pay for her car?<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167824648796\">\n<div data-type=\"problem\" id=\"fs-id1167824648799\">\n<p id=\"fs-id1167824648801\">Laurie has ?46,000 invested in stocks and bonds. The amount invested in stocks is ?8,000 less than three times the amount invested in bonds. How much does Laurie have invested in bonds?<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167833224308\">\n<p id=\"fs-id1167833224310\">?13,500<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167833224315\">\n<div data-type=\"problem\" id=\"fs-id1167836665437\">\n<p id=\"fs-id1167836665439\">Erica earned a total of ?50,450 last year from her two jobs. The amount she earned from her job at the store was ?1,250 more than three times the amount she earned from her job at the college. How much did she earn from her job at the college?<\/p>\n<\/div>\n<\/div>\n<p id=\"fs-id1167833020012\"><strong data-effect=\"bold\">Solve Percent Applications<\/strong><\/p>\n<p id=\"fs-id1167833020018\">In the following exercises, translate and solve.<em data-effect=\"italics\"><\/em><\/p>\n<div data-type=\"exercise\" id=\"fs-id1167836298448\">\n<div data-type=\"problem\" id=\"fs-id1167836298450\">\n<p id=\"fs-id1167836298453\"><span class=\"token\">\u24d0<\/span> What number is 45% of 120? <span class=\"token\">\u24d1<\/span> 81 is 75% of what number? <span class=\"token\">\u24d0<\/span> What percent of 260 is 78?<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836701016\">\n<p id=\"fs-id1167836701018\"><span class=\"token\">\u24d0<\/span> 54 <span class=\"token\">\u24d1<\/span> 108 <span class=\"token\">\u24d0<\/span> 30%<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829811784\">\n<div data-type=\"problem\" id=\"fs-id1167829811786\">\n<p id=\"fs-id1167829811788\"><span class=\"token\">\u24d0<\/span> What number is 65% of 100? <span class=\"token\">\u24d1<\/span> 93 is 75% of what number? <span class=\"token\">\u24d0<\/span> What percent of 215 is 86?<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829878304\">\n<div data-type=\"problem\" id=\"fs-id1167829878306\">\n<p id=\"fs-id1167829878308\"><span class=\"token\">\u24d0<\/span> 250% of 65 is what number? <span class=\"token\">\u24d1<\/span> 8.2% of what amount is ?2.87? <span class=\"token\">\u24d0<\/span> 30 is what percent of 20?<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836704536\">\n<p id=\"fs-id1167836704538\"><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-7c7601fde92978b7d5d8abc21fd18c13_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#54;&#50;&#46;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"39\" style=\"vertical-align: -1px;\" \/><span class=\"token\">\u24d1<\/span> ?35 <span class=\"token\">\u24d0<\/span> 150%<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167833058040\">\n<div data-type=\"problem\" id=\"fs-id1167833058042\">\n<p id=\"fs-id1167833058044\"><span class=\"token\">\u24d0<\/span> 150% of 90 is what number? <span class=\"token\">\u24d1<\/span> 6.4% of what amount is ?2.88? <span class=\"token\">\u24d0<\/span> 50 is what percent of 40?<\/p>\n<\/div>\n<\/div>\n<p id=\"fs-id1167829919871\">In the following exercises, solve.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167829919874\">\n<div data-type=\"problem\" id=\"fs-id1167829919876\">\n<p id=\"fs-id1167829919878\">Geneva treated her parents to dinner at their favorite restaurant. The bill was ?74.25. Geneva wants to leave 16% of the total bill as a tip. How much should the tip be?<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167829693632\">\n<p id=\"fs-id1167836611999\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-db29a9c3358e0b5ca5a78d90a3133605_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#63;&#125;&#49;&#49;&#46;&#56;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"49\" style=\"vertical-align: -1px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836612010\">\n<div data-type=\"problem\" id=\"fs-id1167832999766\">\n<p id=\"fs-id1167832999768\">When Hiro and his co-workers had lunch at a restaurant near their work, the bill was ?90.50. They want to leave 18% of the total bill as a tip. How much should the tip be?<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167833227165\">\n<div data-type=\"problem\" id=\"fs-id1167833227167\">\n<p id=\"fs-id1167833227169\">One serving of oatmeal has 8 grams of fiber, which is 33% of the recommended daily amount. What is the total recommended daily amount of fiber?<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836322669\">\n<p id=\"fs-id1167836322671\">24.2 g<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836322677\">\n<div data-type=\"problem\" id=\"fs-id1167836322679\">\n<p id=\"fs-id1167829691106\">One serving of trail mix has 67 grams of carbohydrates, which is 22% of the recommended daily amount. What is the total recommended daily amount of carbohydrates?<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836576424\">\n<div data-type=\"problem\" id=\"fs-id1167836576426\">\n<p id=\"fs-id1167836576428\">A bacon cheeseburger at a popular fast food restaurant contains 2070 milligrams (mg) of sodium, which is 86% of the recommended daily amount. What is the total recommended daily amount of sodium?<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836476709\">\n<p id=\"fs-id1167836476711\">2407 mg<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836476716\">\n<div data-type=\"problem\" id=\"fs-id1167836476718\">\n<p id=\"fs-id1167836602310\">A grilled chicken salad at a popular fast food restaurant contains 650 milligrams (mg) of sodium, which is 27% of the recommended daily amount. What is the total recommended daily amount of sodium?<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167832940653\">\n<div data-type=\"problem\" id=\"fs-id1167832940655\">\n<p id=\"fs-id1167832940657\">The nutrition fact sheet at a fast food restaurant says the fish sandwich has 380 calories, and 171 calories are from fat. What percent of the total calories is from fat?<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167832940663\">\n<p id=\"fs-id1167829756388\">45%<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829756393\">\n<div data-type=\"problem\" id=\"fs-id1167829756395\">\n<p id=\"fs-id1167829756398\">The nutrition fact sheet at a fast food restaurant says a small portion of chicken nuggets has 190 calories, and 114 calories are from fat. What percent of the total calories is from fat?<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836319645\">\n<div data-type=\"problem\" id=\"fs-id1167836667015\">\n<p id=\"fs-id1167836667017\">Emma gets paid ?3,000 per month. She pays ?750 a month for rent. What percent of her monthly pay goes to rent?<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836667022\">\n<p id=\"fs-id1167836667024\">25%<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836618689\">\n<div data-type=\"problem\" id=\"fs-id1167836618692\">\n<p id=\"fs-id1167836618694\">Dimple gets paid ?3,200 per month. She pays ?960 a month for rent. What percent of her monthly pay goes to rent?<\/p>\n<\/div>\n<\/div>\n<p id=\"fs-id1167836554347\">In the following exercises, solve.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167836554350\">\n<div data-type=\"problem\" id=\"fs-id1167836554352\">\n<p id=\"fs-id1167829893903\">Tamanika received a raise in her hourly pay, from ?15.50 to ?17.36. Find the percent change.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167829624095\">\n<p id=\"fs-id1167829595401\">12%<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829595406\">\n<div data-type=\"problem\" id=\"fs-id1167829595408\">\n<p id=\"fs-id1167829595410\">Ayodele received a raise in her hourly pay, from ?24.50 to ?25.48. Find the percent change.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829695315\">\n<div data-type=\"problem\" id=\"fs-id1167829695317\">\n<p id=\"fs-id1167829695319\">Annual student fees at the University of California rose from about ?4,000 in 2000 to about ?12,000 in 2010. Find the percent change.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167829695325\">\n<p id=\"fs-id1167836521072\">200%<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836521077\">\n<div data-type=\"problem\" id=\"fs-id1167836521079\">\n<p id=\"fs-id1167836521081\">The price of a share of one stock rose from ?12.50 to ?50. Find the percent change.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167833350404\">\n<div data-type=\"problem\" id=\"fs-id1167833350406\">\n<p id=\"fs-id1167833350408\">A grocery store reduced the price of a loaf of bread from ?2.80 to ?2.73. Find the percent change.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167829755991\">\n<p id=\"fs-id1167829755993\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-5f3449c2385224c80040aa23ae092b45_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#46;&#53;&#37;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"35\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836531527\">\n<div data-type=\"problem\" id=\"fs-id1167836531529\">\n<p id=\"fs-id1167836531531\">The price of a share of one stock fell from ?8.75 to ?8.54. Find the percent change.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167826211784\">\n<div data-type=\"problem\" id=\"fs-id1167826211786\">\n<p id=\"fs-id1167826211788\">Hernando\u2019s salary was ?49,500 last year. This year his salary was cut to ?44,055. Find the percent change.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167833052534\">\n<p id=\"fs-id1167833052537\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-05e8a60bf94a15df9864f54e27316be5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#49;&#37;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"30\" style=\"vertical-align: -1px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836576058\">\n<div data-type=\"problem\" id=\"fs-id1167836576060\">\n<p id=\"fs-id1167836576062\">In ten years, the population of Detroit fell from 950,000 to about 712,500. Find the percent change.<\/p>\n<\/div>\n<\/div>\n<p id=\"fs-id1167829721247\">In the following exercises, find <span class=\"token\">\u24d0<\/span> the amount of discount and <span class=\"token\">\u24d1<\/span> the sale price.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167829740266\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167829740268\">\n<p id=\"fs-id1167836531586\">Janelle bought a beach chair on sale at 60% off. The original price was ?44.95.<\/p>\n<\/div>\n<div data-type=\"solution\">\n<p id=\"fs-id1167836541940\"><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-efa83b2f5b8b05243594d4606d91f3f5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#63;&#125;&#50;&#54;&#46;&#57;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"49\" style=\"vertical-align: 0px;\" \/><span class=\"token\">\u24d1<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-03d0b1a8ced66929e02833fa1d232d44_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#63;&#125;&#49;&#55;&#46;&#57;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"49\" style=\"vertical-align: -1px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829752238\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167829752241\">\n<p id=\"fs-id1167829752243\">Errol bought a skateboard helmet on sale at 40% off. The original price was ?49.95.<\/p>\n<\/div>\n<\/div>\n<p id=\"fs-id1167829691157\">In the following exercises, find <span class=\"token\">\u24d0<\/span> the amount of discount and <span class=\"token\">\u24d1<\/span> the discount rate (Round to the nearest tenth of a percent if needed.)<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167829595570\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167829595572\">\n<p id=\"fs-id1167836449693\">Larry and Donna bought a sofa at the sale price of ?1,344. The original price of the sofa was ?1,920.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836449697\">\n<p id=\"fs-id1167836449700\"><span class=\"token\">\u24d0<\/span> ?576 <span class=\"token\">\u24d1<\/span> 30%<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829811898\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167829811900\">\n<p id=\"fs-id1167829811902\">Hiroshi bought a lawnmower at the sale price of ?240. The original price of the lawnmower is ?300.<\/p>\n<\/div>\n<\/div>\n<p id=\"fs-id1167832937184\">In the following exercises, find <span class=\"token\">\u24d0<\/span> the amount of the mark-up and <span class=\"token\">\u24d1<\/span> the list price.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167832999647\">\n<div data-type=\"problem\" id=\"fs-id1167832999649\">\n<p id=\"fs-id1167832999651\">Daria bought a bracelet at original cost ?16 to sell in her handicraft store. She marked the price up 45%. What was the list price of the bracelet?<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836535896\">\n<p id=\"fs-id1167836535898\"><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-675aa1ba29fddf704f47e4468a7cc1a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#63;&#125;&#55;&#46;&#50;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"40\" style=\"vertical-align: 0px;\" \/><span class=\"token\">\u24d1<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-cc4b1de7d4028127e861f220c4330d75_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#63;&#125;&#50;&#51;&#46;&#50;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"49\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167824734807\">\n<div data-type=\"problem\" id=\"fs-id1167824734809\">\n<p id=\"fs-id1167824734811\">Regina bought a handmade quilt at original cost ?120 to sell in her quilt store. She marked the price up 55%. What was the list price of the quilt?<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836700655\">\n<div data-type=\"problem\" id=\"fs-id1167836700657\">\n<p id=\"fs-id1167836700660\">Tom paid ?0.60 a pound for tomatoes to sell at his produce store. He added a 33% mark-up. What price did he charge his customers for the tomatoes?<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836621799\">\n<p id=\"fs-id1167833057683\"><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-1549e70202b5b7473d5e3d118bac3b8b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#63;&#125;&#48;&#46;&#50;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"40\" style=\"vertical-align: 0px;\" \/><span class=\"token\">\u24d1<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-370a14986d2a56b3cf138e4206a4ed79_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#63;&#125;&#48;&#46;&#56;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"40\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167833346738\">\n<div data-type=\"problem\" id=\"fs-id1167833346740\">\n<p id=\"fs-id1167833346742\">Flora paid her supplier ?0.74 a stem for roses to sell at her flower shop. She added an 85% mark-up. What price did she charge her customers for the roses?<\/p>\n<\/div>\n<\/div>\n<p id=\"fs-id1167833310740\"><strong data-effect=\"bold\">Solve Simple Interest Applications<\/strong><em data-effect=\"italics\"><\/em><\/p>\n<p id=\"fs-id1167833310749\">In the following exercises, solve.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167829879268\">\n<div data-type=\"problem\" id=\"fs-id1167829879270\">\n<p id=\"fs-id1167829879273\">Casey deposited ?1,450 in a bank account that earned simple interest at an interest rate of 4%. How much interest was earned in two years?<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167829879278\">\n<p id=\"fs-id1167829879280\">?116<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836551570\">\n<div data-type=\"problem\" id=\"fs-id1167836551572\">\n<p id=\"fs-id1167836551574\">Terrence deposited ?5,720 in a bank account that earned simple interest at an interest rate of 6%. How much interest was earned in four years?<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167833054990\">\n<div data-type=\"problem\" id=\"fs-id1167833054992\">\n<p id=\"fs-id1167836387520\">Robin deposited ?31,000 in a bank account that earned simple interest at an interest rate of 5.2%. How much interest was earned in three years?<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836387526\">\n<p id=\"fs-id1167836387528\">?4836<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829785461\">\n<div data-type=\"problem\" id=\"fs-id1167829785463\">\n<p id=\"fs-id1167829785465\">Carleen deposited ?16,400 in a bank account that earned simple interest at an interest rate of 3.9% How much interest was earned in eight years?<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836575190\">\n<div data-type=\"problem\" id=\"fs-id1167836575192\">\n<p id=\"fs-id1167826206379\">Hilaria borrowed ?8,000 from her grandfather to pay for college. Five years later, she paid him back the ?8,000, plus ?1,200 interest. What was the rate of simple interest?<\/p>\n<\/div>\n<div data-type=\"solution\">\n<p id=\"fs-id1167826206387\">3%<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167833369027\">\n<div data-type=\"problem\" id=\"fs-id1167833369029\">\n<p id=\"fs-id1167833369031\">Kenneth lent his niece ?1,200 to buy a computer. Two years later, she paid him back the ?1,200, plus ?96 interest. What was the rate of simple interest?<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836391228\">\n<div data-type=\"problem\" id=\"fs-id1167836391230\">\n<p id=\"fs-id1167836391232\">Lebron lent his daughter ?20,000 to help her buy a condominium. When she sold the condominium four years later, she paid him the ?20,000, plus ?3,000 interest. What was the rate of simple interest?<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836598890\">\n<p id=\"fs-id1167836598892\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-9f813346793ba9afcac98bde5c29ecb1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#46;&#55;&#53;&#37;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829790280\">\n<div data-type=\"problem\" id=\"fs-id1167829790282\">\n<p id=\"fs-id1167829790285\">Pablo borrowed ?50,000 to start a business. Three years later, he repaid the ?50,000, plus ?9,375 interest. What was the rate of simple interest?<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167826171978\">\n<div data-type=\"problem\" id=\"fs-id1167826146791\">\n<p id=\"fs-id1167826146793\">In 10 years, a bank account that paid 5.25% simple interest earned ?18,375 interest. What was the principal of the account?<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836605943\">\n<p id=\"fs-id1167836605946\">?35,000<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836605951\">\n<div data-type=\"problem\" id=\"fs-id1167836605953\">\n<p id=\"fs-id1167836529597\">In 25 years, a bond that paid 4.75% simple interest earned ?2,375 interest. What was the principal of the bond?<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167832930332\">\n<div data-type=\"problem\" id=\"fs-id1167832930334\">\n<p id=\"fs-id1167832930336\">Joshua\u2019s computer loan statement said he would pay ?1,244.34 in simple interest for a three-year loan at 12.4%. How much did Joshua borrow to buy the computer?<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836580097\">\n<p id=\"fs-id1167836580099\">?3345<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836580104\">\n<div data-type=\"problem\" id=\"fs-id1167836580106\">\n<p id=\"fs-id1167829754765\">Margaret\u2019s car loan statement said she would pay ?7,683.20 in simple interest for a five-year loan at 9.8%. How much did Margaret borrow to buy the car?<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"everyday\" data-depth=\"2\" id=\"fs-id1167833347102\">\n<h4 data-type=\"title\">Everyday Math<\/h4>\n<div data-type=\"exercise\" id=\"fs-id1167833347108\">\n<div data-type=\"problem\" id=\"fs-id1167829741376\">\n<p id=\"fs-id1167829741378\"><strong data-effect=\"bold\">Tipping<\/strong> At the campus coffee cart, a medium coffee costs ?1.65. MaryAnne brings ?2.00 with her when she buys a cup of coffee and leaves the change as a tip. What percent tip does she leave?<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167833349758\">\n<p id=\"fs-id1167833349760\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-a4ea0f98576e457a83627fcbf4370f73_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#55;&#46;&#53;&#37;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"30\" style=\"vertical-align: -1px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167833082221\">\n<div data-type=\"problem\" id=\"fs-id1167833082223\">\n<p id=\"fs-id1167833082225\"><strong data-effect=\"bold\">Tipping<\/strong> Four friends went out to lunch and the bill came to ?53.75 They decided to add enough tip to make a total of ?64, so that they could easily split the bill evenly among themselves. What percent tip did they leave?<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"writing\" data-depth=\"2\" id=\"fs-id1167833385993\">\n<h4 data-type=\"title\">Writing Exercises<\/h4>\n<div data-type=\"exercise\" id=\"fs-id1167833385999\">\n<div data-type=\"problem\" id=\"fs-id1167833386001\">\n<p id=\"fs-id1167833386004\">What has been your past experience solving word problems? Where do you see yourself moving forward?<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167829850147\">\n<p id=\"fs-id1167829850149\">Answers will vary.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829850154\">\n<div data-type=\"problem\" id=\"fs-id1167829850156\">\n<p id=\"fs-id1167836515997\">Without solving the problem \u201c44 is 80% of what number\u201d think about what the solution might be. Should it be a number that is greater than 44 or less than 44? Explain your reasoning.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836516006\">\n<div data-type=\"problem\" id=\"fs-id1167836516008\">\n<p id=\"fs-id1167836630152\">After returning from vacation, Alex said he should have packed 50% fewer shorts and 200% more shirts. Explain what Alex meant.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836630157\">\n<p id=\"fs-id1167836630159\">Answers will vary.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836610897\">\n<div data-type=\"problem\" id=\"fs-id1167836610899\">\n<p id=\"fs-id1167836610901\">Because of road construction in one city, commuters were advised to plan that their Monday morning commute would take 150% of their usual commuting time. Explain what this means.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"bc-section section\" data-depth=\"2\" id=\"fs-id1167836527743\">\n<h4 data-type=\"title\">Self Check<\/h4>\n<p id=\"fs-id1167836692505\"><span class=\"token\">\u24d0<\/span> After completing the exercises, use this checklist to evaluate your mastery of the objective of this section.<\/p>\n<p><span data-type=\"media\" id=\"fs-id1167836692516\" data-alt=\"This table has four columns and five rows. The first row is a header and it labels each column, \u201cI can\u2026\u201d, \u201cConfidently,\u201d \u201cWith some help,\u201d and \u201cNo-I don\u2019t get it!\u201d In row 2, the I can was use a problem-solving strategy for word problems. In row 3, the I can was solve number problems. In row 4, the I can was solve percent applications. In row 5, the I can was solve simple interest applications.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_02_02_201_img_new-1.jpg\" data-media-type=\"image\/jpeg\" alt=\"This table has four columns and five rows. The first row is a header and it labels each column, \u201cI can\u2026\u201d, \u201cConfidently,\u201d \u201cWith some help,\u201d and \u201cNo-I don\u2019t get it!\u201d In row 2, the I can was use a problem-solving strategy for word problems. In row 3, the I can was solve number problems. In row 4, the I can was solve percent applications. In row 5, the I can was solve simple interest applications.\" \/><\/span><\/p>\n<p><span class=\"token\">\u24d1<\/span> After reviewing this checklist, what will you do to become confident for all objectives?<\/p>\n<\/div>\n<\/div>\n","protected":false},"author":103,"menu_order":3,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1200","chapter","type-chapter","status-publish","hentry"],"part":991,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-json\/pressbooks\/v2\/chapters\/1200","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-json\/wp\/v2\/users\/103"}],"version-history":[{"count":1,"href":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-json\/pressbooks\/v2\/chapters\/1200\/revisions"}],"predecessor-version":[{"id":15151,"href":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-json\/pressbooks\/v2\/chapters\/1200\/revisions\/15151"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-json\/pressbooks\/v2\/parts\/991"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-json\/pressbooks\/v2\/chapters\/1200\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-json\/wp\/v2\/media?parent=1200"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-json\/pressbooks\/v2\/chapter-type?post=1200"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-json\/wp\/v2\/contributor?post=1200"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-json\/wp\/v2\/license?post=1200"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}