{"id":921,"date":"2021-05-19T16:42:58","date_gmt":"2021-05-19T16:42:58","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/math53\/chapter\/solve-a-formula-for-a-specific-variable\/"},"modified":"2023-06-05T18:54:56","modified_gmt":"2023-06-05T18:54:56","slug":"solve-a-formula-for-a-specific-variable","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/math53\/chapter\/solve-a-formula-for-a-specific-variable\/","title":{"raw":"3.6 Solve a Formula for a Specific Variable","rendered":"3.6 Solve a Formula for a Specific Variable"},"content":{"raw":"[latexpage]\r\n<div class=\"textbox textbox--learning-objectives\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Learning Objectives<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nBy the end of this section, you will be able to:\r\n<ul>\r\n \t<li>Use the Distance, Rate, and Time formula<\/li>\r\n \t<li>Solve a formula for a specific variable<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>\r\n<h1 data-type=\"title\">Use the Distance, Rate, and Time Formula<\/h1>\r\n<p id=\"fs-id1168342181224\">One formula you will use often in algebra and in everyday life is the formula for distance traveled by an object moving at a constant rate. Rate is an equivalent word for \u201cspeed.\u201d The basic idea of rate may already be familiar to you. Do you know what distance you travel if you drive at a steady rate of 60 miles per hour for 2 hours? (This might happen if you use your car\u2019s cruise control while driving on the highway.) If you said 120 miles, you already know how to use this formula!<\/p>\r\n\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Distance, Rate, and Time<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<p id=\"fs-id1168345633583\">For an object moving at a uniform (constant) rate, the distance traveled, the elapsed time, and the rate are related by the formula:<\/p>\r\n\r\n<div id=\"fs-id1166502309552\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(\\begin{array}{ccccccccc}d=rt\\hfill &amp; &amp; &amp; \\hfill \\text{where}\\hfill &amp; &amp; &amp; \\hfill d&amp; =\\hfill &amp; \\text{distance}\\hfill \\\\ &amp; &amp; &amp; &amp; &amp; &amp; \\hfill r&amp; =\\hfill &amp; \\text{rate}\\hfill \\\\ &amp; &amp; &amp; &amp; &amp; &amp; \\hfill t&amp; =\\hfill &amp; \\text{time}\\hfill \\end{array}\\)<\/div>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1168345636448\">We will use the Strategy for Solving Applications that we used earlier in this chapter. When our problem requires a formula, we change Step 4. In place of writing a sentence, we write the appropriate formula. We write the revised steps here for reference.<\/p>\r\n\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">HOW TO: Solve an application (with a formula).<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<ol id=\"fs-id1169751874724\" class=\"stepwise\" type=\"1\">\r\n \t<li><strong data-effect=\"bold\">Read<\/strong> the problem. Make sure all the words and ideas are understood.<\/li>\r\n \t<li><strong data-effect=\"bold\">Identify<\/strong> what we are looking for.<\/li>\r\n \t<li><strong data-effect=\"bold\">Name<\/strong> what we are looking for. Choose a variable to represent that quantity.<\/li>\r\n \t<li><strong data-effect=\"bold\">Translate<\/strong> into an equation. Write the appropriate formula for the situation. Substitute in the given information.<\/li>\r\n \t<li><strong data-effect=\"bold\">Solve<\/strong> the equation using good algebra techniques.<\/li>\r\n \t<li><strong data-effect=\"bold\">Check<\/strong> the answer in the problem and make sure it makes sense.<\/li>\r\n \t<li><strong data-effect=\"bold\">Answer<\/strong> the question with a complete sentence.<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1168345529730\">You may want to create a mini-chart to summarize the information in the problem. See the chart in this first example.<\/p>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1168345384975\" data-type=\"problem\">\r\n<p id=\"fs-id1168345276335\">Jamal rides his bike at a uniform rate of 12 miles per hour for \\(3\\frac{1}{2}\\) hours. What distance has he traveled?<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1168341892523\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<table id=\"fs-id1167270960754\" class=\"unnumbered unstyled\" style=\"width: 100%\" summary=\"This figure is a table that has two columns and seven rows. The first column is a header column, and it contains the names and numbers of each step. The second column contains math answers. On the top row of the table, the first cell on the left reads: \u201cStep 1. Read the problem.\u201d In the second row of the table, the first cell on the left reads: \u201cStep 2. Identify what you are looking for.\u201d The second cell contains the answer \u201cdistance traveled\u201d. In the third row of the table, the first cell on the left reads: \u201cStep 3. Name: Choose a variable to represent it.\u201d The second cell contains the answer: \u201clet d equal distance\u201d. In the fourth row of the table, the first cell on the left reads: \u201cStep 4. Translate: Write the appropriate formula. Substitute in the given information.\u201d The second cell contains the formula d equals rt. Below this is a table with one column of three cells. From top to bottom, the cells reads: \u201cd equals ?\u201d, \u201cr equals 12 mph\u201d, and \u201ct equals 3 and one-half hours\u201d. Below this is the formula with the given information substituted in: d equals 12 times 3 and a half. In the fifth row of the table, the first cell on the left reads: \u201cStep 5. Solve the equation.\u201d The second cell contains the equation d equals 42 miles. In the sixth row of the table, the first cell on the left reads: \u201cStep 6. Check. Does 42 miles make sense? Jamal rides: 12 miles in 1 hour, 24 miles in 2 hours, 36 miles in 3 hours, 48 miles in 4 hours.\u201d There is an arrow pointing between 3 and 4 hours, and it indicates: \u201c42 miles in 3 and a half hours is reasonable.\u201d In the seventh row of the table, the first cell on the left reads: \u201cAnswer the question with a complete sentence.\u201d The second cell contains the sentence: \u201cJamal rode 42 miles.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td><strong data-effect=\"bold\">Step 1. Read<\/strong> the problem.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong data-effect=\"bold\">Step 2. Identify<\/strong> what you are looking for.<\/td>\r\n<td>distance traveled<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong data-effect=\"bold\">Step 3. Name.<\/strong> Choose a variable to represent it.<\/td>\r\n<td>Let <em data-effect=\"italics\">d<\/em> = distance.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong data-effect=\"bold\">Step 4. Translate:<\/strong> Write the appropriate formula.<\/td>\r\n<td>\\(d=rt\\)\r\n\r\n[latex]d=?[\/latex]\r\n\r\n[latex]r=12 [\/latex] mph\r\n\r\n[latex]t=3\\frac{1}{2} [\/latex] hours<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Substitute in the given information.<\/td>\r\n<td>\\(d=12\\cdot 3\\frac{1}{2}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong data-effect=\"bold\">Step 5. Solve<\/strong> the equation.<\/td>\r\n<td>\\(d=42\\) miles<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong data-effect=\"bold\">Step 6. Check<\/strong>\r\n\r\nDoes 42 miles make sense?\r\n\r\nJamal rides:<\/td>\r\n<td>[latex]\\\\12 \\text{ miles in } 1 \\text{ hour}\\\\\r\n24 \\text{miles in } 2 \\text{ hours}[\/latex]\r\n[latex] \\begin{array} \\quad&amp;\\left\\ \\begin{tabular}{@{}l@{}} 36 miles in 3 hours \\\\ 48 miles in 4 hours \\end{tabular} \\right\\} \\end{array} \\text{42 miles in } 3\\frac{1}{2} \\text{hours seems reasonable}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong data-effect=\"bold\">Step 7. Answer the question<\/strong> with a complete sentence.<\/td>\r\n<td>Jamal rode 42 miles.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1168345418079\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1168341907611\" data-type=\"exercise\">\r\n<div id=\"fs-id1168345302709\" data-type=\"problem\">\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 1.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1168345302709\" data-type=\"problem\">\r\n<p id=\"fs-id1168345691673\">Lindsay drove for \\(5\\frac{1}{2}\\) hours at 60 miles per hour. How much distance did she travel?<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1168345461727\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\r\n<p id=\"fs-id1168345451606\">330 miles<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 1.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1168345557101\" data-type=\"problem\">\r\n<p id=\"fs-id1168345215800\">Trinh walked for \\(2\\frac{1}{3}\\) hours at 3 miles per hour. How far did she walk?<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1168345240061\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\r\n<p id=\"fs-id1168345262359\">7 miles<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1168345454045\" data-type=\"problem\">\r\n<p id=\"fs-id1168345385591\">Rey is planning to drive from his house in Saskatoon to visit his grandmother in Winnipeg, a distance of 798 km. If he can drive at a steady rate of 76 km per hour, how many hours will the trip take?<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1168342180736\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<table id=\"fs-id1167271046130\" style=\"width: 100%\" summary=\"This figure is a table that has two columns and seven rows. The first column is a header column, and it contains the names and numbers of each step. The second column contains math answers. On the top row of the table, the first cell on the left reads: \u201cStep 1. Read the problem.\u201d In the second row of the table, the first cell on the left reads: \u201cStep 2. Identify what you are looking for.\u201d The second cell contains the answer \u201chow many hours (time)\u201d. In the third row of the table, the first cell on the left reads: \u201cStep 3. Name: Choose a variable to represent it.\u201d The second cell contains the answer: \u201clet t equal time\u201d. Below this is a table with one column of three cells. From top to bottom, the cells reads: \u201cd equals 520 miles\u201d, \u201cr equals 65 mph\u201d, and \u201ct equals ? hours\u201d. In the fourth row of the table, the first cell on the left reads: \u201cStep 4. Translate: Write the appropriate formula. Substitute in the given information.\u201d The second cell contains the formula d equals rt. Below this is the formula with the given information substituted in: 520 equals 65t. In the fifth row of the table, the first cell on the left reads: \u201cStep 5. Solve the equation.\u201d The second cell contains the equation t equals 8. In the sixth row of the table, the first cell on the left reads: \u201cStep 6. Check. Substitute the numbers into the formula and make sure the result is a true statement.\u201d Below this is the equation d equals rt. Below this is the equation 520 might equal 65 times 8. Below this is the equation 520 equals 520, with a check mark next to it. In the seventh row of the table, the first cell on the left reads: \u201cAnswer the question with a complete sentence. Ray\u2019s trip will take 8 hours.\u201d\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td><strong data-effect=\"bold\">Step 1. Read<\/strong> the problem.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong data-effect=\"bold\">Step 2. Identify<\/strong> what you are looking for.<\/td>\r\n<td>How many hours (time)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong data-effect=\"bold\">Step 3. Name.<\/strong>\r\nChoose a variable to represent it.<\/td>\r\n<td>Let <em data-effect=\"italics\">t<\/em> = time.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>d = 798 km\r\n\r\nr = 76 km\/h\r\n\r\nt = ? hours<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong data-effect=\"bold\">Step 4. Translate.<\/strong>\r\nWrite the appropriate formula.<\/td>\r\n<td data-valign=\"bottom\">\\(\\phantom{\\rule{1em}{0ex}}d=rt\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Substitute in the given information.<\/td>\r\n<td>\\(798=76t\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong data-effect=\"bold\">Step 5. Solve<\/strong> the equation.<\/td>\r\n<td>\\(\\phantom{\\rule{1.2em}{0ex}}t=10.5\\) hours<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong data-effect=\"bold\">Step 6. Check.<\/strong> Substitute the numbers into\r\nthe formula and make sure the result is a\r\ntrue statement.<\/td>\r\n<td>\\(\\begin{array}{ccc}\\hfill d&amp; =\\hfill &amp; rt\\hfill \\\\ \\hfill 798&amp; \\stackrel{?}{=}\\hfill &amp; 76\\cdot 10.5\\hfill \\\\ \\hfill 798&amp; =\\hfill &amp; 798\\hfill \\end{array}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td colspan=\"2\"><strong data-effect=\"bold\">Step 7. Answer<\/strong> the question with a complete sentence. Rey\u2019s trip will take 10.5 hours.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1168342171016\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1168345250678\" data-type=\"exercise\">\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 2.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1168345450632\" data-type=\"problem\">\r\n\r\nLee wants to drive from Kamloops to his brother\u2019s apartment in Banff, a distance of 495 km. If he drives at a steady rate of 90 km\/h, how many hours will the trip take?\r\n\r\n<\/div>\r\n<div id=\"fs-id1168345302714\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\r\n<p id=\"fs-id1168345407862\">5 1\/2 hours<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 2.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div data-type=\"problem\">\r\n<p id=\"fs-id1168345327714\">Yesenia is 168 km from Toronto. If she needs to be in Toronto in 2 hours, at what rate does she need to drive?<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1168345636492\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\r\n<p id=\"fs-id1168345270054\">84 km\/h<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<h1 data-type=\"title\">Solve a Formula for a Specific Variable<\/h1>\r\n<p id=\"fs-id1168345638743\">You are probably familiar with some geometry formulas. A formula is a mathematical description of the relationship between variables. Formulas are also used in the sciences, such as chemistry, physics, and biology. In medicine they are used for calculations for dispensing medicine or determining body mass index. Spreadsheet programs rely on formulas to make calculations. It is important to be familiar with formulas and be able to manipulate them easily.<\/p>\r\n<p id=\"fs-id1168345376761\">In <a class=\"autogenerated-content\" href=\"#fs-id1168345529730\">(Example 1)<\/a> and <a class=\"autogenerated-content\" href=\"#fs-id1168345454045\">(Example 2)<\/a>, we used the formula \\(d=rt\\). This formula gives the value of \\(d\\), distance, when you substitute in the values of \\(r\\phantom{\\rule{0.2em}{0ex}}\\text{and}\\phantom{\\rule{0.2em}{0ex}}t\\), the rate and time. But in <a class=\"autogenerated-content\" href=\"#fs-id1168345454045\">(Example 2)<\/a>, we had to find the value of \\(t\\). We substituted in values of \\(d\\phantom{\\rule{0.2em}{0ex}}\\text{and}\\phantom{\\rule{0.2em}{0ex}}r\\) and then used algebra to solve for \\(t\\). If you had to do this often, you might wonder why there is not a formula that gives the value of \\(t\\) when you substitute in the values of \\(d\\phantom{\\rule{0.2em}{0ex}}\\text{and}\\phantom{\\rule{0.2em}{0ex}}r\\). We can make a formula like this by solving the formula \\(d=rt\\) for \\(t\\).<\/p>\r\n<p id=\"fs-id1168345449343\">To solve a formula for a specific variable means to isolate that variable on one side of the equals sign with a coefficient of 1. All other variables and constants are on the other side of the equals sign. To see how to solve a formula for a specific variable, we will start with the distance, rate and time formula.<\/p>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 3<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1168345255240\" data-type=\"problem\">\r\n<p id=\"fs-id1168345455465\">Solve the formula \\(d=rt\\) for \\(t\\):<\/p>\r\n\r\n<ol id=\"fs-id1169751926961\" class=\"circled\" type=\"a\">\r\n \t<li>when \\(d=520\\) km and \\(r=65\\) km\/hr<\/li>\r\n \t<li>in general<\/li>\r\n<\/ol>\r\n<\/div>\r\n<div id=\"fs-id1168345329250\" data-type=\"solution\">\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\"><\/div>\r\n<p id=\"fs-id1168345427139\">We will write the solutions side-by-side to demonstrate that solving a formula in general uses the same steps as when we have numbers to substitute.<\/p>\r\n\r\n<table id=\"fs-id1169149033323\" class=\"unnumbered unstyled\" summary=\"This is a table that has five rows and four columns. The instructions and math within it demonstrate the solving a formula is done the same way for a formula in general and for when actual values are substituted into the formula. The first row, which is a header row, has only two cells: one that spans the first two columns, and one that spans the third and fourth columns. In the header row, the first cell to the left reads: \u201c(a) when d equals 520 and r equals 65.\u201d The second cell reads: \u201c(b) in general.\u201d Below the header row, the first and third columns contain written instructions, and the second and fourth columns show math. In the second row, the first cell reads: \u201cWrite the formula.\u201d The second cell contains the equation d equals r times t. The third cell reads: \u201cWrite the formula.\u201d The fourth cell contains the equation d equals r times t. In the third row, the first cell to the left reads: \u201cSubstitute.\u201d The second cell contains the equation 520 equals 65 times t. The third and fourth cells are left blank. In the fourth row, the first cell to the left reads: \u201cDivide, to isolate t.\u201d The second cell contains the equation 520 over 65 equals 65t over 65. The third cell reads: \u201cDivide, to isolate t.\u201d The fourth cell contains the equation d over r equals the product r times t over r. In the last row, the first cell to the left reads: \u201cSimplify.\u201d The second cell contains the answer to the equation: 8 equals t. The third cell reads: \u201cSimplify.\u201d The fourth cell contains the equation d over r equals t.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 401.406px\" colspan=\"2\">a) when \\(d=520\\) km and \\(r=65\\) km\/hr<\/td>\r\n<td style=\"width: 422.406px\" colspan=\"4\">b) in general<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 147.406px\">Write the formula.<\/td>\r\n<td style=\"width: 239.406px\">\\(\\phantom{\\rule{1em}{0ex}}d=rt\\)<\/td>\r\n<td style=\"width: 225.406px\" colspan=\"3\">Write the formula.<\/td>\r\n<td style=\"width: 182.406px\">\\(d=rt\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 147.406px\">Substitute.<\/td>\r\n<td style=\"width: 239.406px\">\\(520=65t\\)<\/td>\r\n<td style=\"width: 225.406px\" colspan=\"3\"><\/td>\r\n<td style=\"width: 182.406px\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 147.406px\">Divide, to isolate \\(t\\).<\/td>\r\n<td style=\"width: 239.406px\">\\(\\frac{520}{65}=\\frac{65t}{65}\\)<\/td>\r\n<td style=\"width: 225.406px\" colspan=\"3\">Divide, to isolate \\(t\\).<\/td>\r\n<td style=\"width: 182.406px\">\\(\\frac{d}{r}=\\frac{rt}{r}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 147.406px\">Simplify.<\/td>\r\n<td style=\"width: 239.406px\">\\(\\phantom{\\rule{1.2em}{0ex}}8=t\\)\r\n\r\n[latex]t=8[\/latex] hours<\/td>\r\n<td style=\"width: 225.406px\" colspan=\"3\">Simplify.<\/td>\r\n<td style=\"width: 182.406px\">\\(\\frac{d}{r}=t\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p id=\"fs-id1168345511097\">We say the formula \\(t=\\frac{d}{r}\\) is solved for \\(t\\).<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1168345211803\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1168345228073\" data-type=\"exercise\">\r\n<div id=\"fs-id1168345511495\" data-type=\"problem\">\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 3.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1168345511495\" data-type=\"problem\">\r\n<p id=\"fs-id1168345303203\">Solve the formula \\(d=rt\\) for \\(r\\):<\/p>\r\n<p id=\"fs-id1168345545931\">a) when \\(d=180\\phantom{\\rule{0.2em}{0ex}}\\text{km and}\\phantom{\\rule{0.2em}{0ex}}t=4 \\) hr\u00a0 b) in general<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1168345325302\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\r\n<p id=\"fs-id1168341853951\">a) \\(r=45\\) km\/hr b) \\(r=\\frac{d}{t}\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 3.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1168345287977\" data-type=\"problem\">\r\n<p id=\"fs-id1168345473398\">Solve the formula \\(d=rt\\) for \\(r\\):<\/p>\r\n<p id=\"fs-id1168345194497\">a) when \\(d=780\\phantom{\\rule{0.2em}{0ex}}\\text{km and}\\phantom{\\rule{0.2em}{0ex}}t=12\\) hr\u00a0 b) in general<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1168345217002\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\r\n<p id=\"fs-id1168341959893\">a) \\(r=65\\) km\/hr\u00a0 b) \\(r=\\frac{d}{t}\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1168345325302\" data-type=\"solution\">\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 4<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1168341863632\" data-type=\"problem\">\r\n<p id=\"fs-id1168345433028\">Solve the formula \\(A=\\frac{1}{2}bh\\) for \\(h\\):<\/p>\r\na) when \\(A=90\\) and \\(b=15\\) b) in general\r\n\r\n<\/div>\r\n<div id=\"fs-id1168345461758\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<table id=\"eip-id1168463862046\" class=\"unnumbered unstyled\" summary=\"This figure is a table that has six rows and four columns. It shows the written instructions and the math for solving a formula when specific values are given, and for solving the formula in general. The first row, which is a header row, has only two cells: one that spans the first two columns, and one that spans the third and fourth columns. In the header row, the first cell to the left reads: \u201c(a) when A equals 90 and b equals 15.\u201d The second cell reads: \u201c(b) in general.\u201d Below the header row, the first and third columns contain written instructions, and the second and fourth columns show math. In the second row, the first cell reads: \u201cWrite the formula.\u201d The second cell contains the equation A equals \u00bd times b times h. The third cell reads: \u201cWrite the formula.\u201d The fourth cell contains the equation A equals \u00bd times b times h. In the third row, the first cell to the left reads: \u201cSubstitute.\u201d The second cell contains the equation 90 equals \u00bd times 15 times h, with 90 and 15 written in red. The third and fourth cells are left blank. In the fourth row, the first cell to the left reads: \u201cClear the fractions.\u201d The second cell contains the equation 2 times 90 equals 2 times \u00bd times 15 times h, with \u201c2 times\u201d written in red on both sides. The third cell reads: \u201cClear the fractions.\u201d The fourth cell contains the equation 2 times A equals 2 times \u00bd times b times h, with \u201c2 times\u201d written in red on both sides. In the fifth row, the first cell to the left reads: \u201cSimplify.\u201d The second cell contains the equation 180 equals 15 times h. The third cell reads: \u201cSimplify.\u201d The fourth cell contains the equation 2 times A equals b times h. In the last row, the first cell to the left reads: \u201cSolve for h.\u201d The second cell contains the solution to the equation: 12 equals h. The third cell reads: \u201cSolve for h.\u201d The fourth cell contains the solution to the equation: the product 2 times A over b equals h.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 295.406px\" colspan=\"2\">a) when \\(A=90\\) and \\(b=15\\)<\/td>\r\n<td style=\"width: 512.406px\" colspan=\"4\">b) in general<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 128.406px\">Write the formula.<\/td>\r\n<td style=\"width: 152.406px\"><span id=\"eip-id1168463859550\" data-type=\"media\" data-alt=\".\">[latex]A=\\frac{1}{2}bh[\/latex]<\/span><\/td>\r\n<td style=\"width: 335.406px\" colspan=\"3\">Write the formula.<\/td>\r\n<td style=\"width: 162.406px\"><span id=\"eip-id1168463859564\" data-type=\"media\" data-alt=\".\">[latex]A=\\frac{1}{2} bh[\/latex]<\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 128.406px\">Substitute.<\/td>\r\n<td style=\"width: 152.406px\">[latex]90=\\frac{1}{2} \\cdot \\textcolor{red}{15} \\cdot h[\/latex]<\/td>\r\n<td style=\"width: 335.406px\" colspan=\"3\"><\/td>\r\n<td style=\"width: 162.406px\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 128.406px\">Clear the fractions.<\/td>\r\n<td style=\"width: 152.406px\"><span id=\"eip-id1168463859603\" data-type=\"media\" data-alt=\".\">\r\n[latex]\\textcolor{red}{2} \\cdot 90 = \\textcolor{red}{2} \\cdot \\frac{1}{2} 15h[\/latex]<\/span><\/td>\r\n<td style=\"width: 335.406px\" colspan=\"3\">Clear the fractions.<\/td>\r\n<td style=\"width: 162.406px\"><span id=\"eip-id1168463819926\" data-type=\"media\" data-alt=\".\">[latex]\\textcolor{red}{2} \\cdot A = \\textcolor{red}{2} \\cdot \\frac{1}{2} bh[\/latex]<\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 128.406px\">Simplify.<\/td>\r\n<td style=\"width: 152.406px\"><span id=\"eip-id1168463819943\" data-type=\"media\" data-alt=\".\">[latex]180=15h[\/latex]<\/span><\/td>\r\n<td style=\"width: 335.406px\" colspan=\"3\">Simplify.<\/td>\r\n<td style=\"width: 162.406px\"><span id=\"eip-id1168463819957\" data-type=\"media\" data-alt=\".\">[latex]2A=bh[\/latex]<\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 128.406px\">Solve for \\(h\\).<\/td>\r\n<td style=\"width: 152.406px\"><span id=\"eip-id1168463819979\" data-type=\"media\" data-alt=\".\">[latex]12=h[\/latex]<\/span><\/td>\r\n<td style=\"width: 335.406px\" colspan=\"3\">Solve for \\(h\\).<\/td>\r\n<td style=\"width: 162.406px\"><span id=\"eip-id1168463819997\" data-type=\"media\" data-alt=\".\">[latex]\\frac{2A}{b} = h[\/latex]<\/span><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p id=\"fs-id1168345723921\">We can now find the height of a triangle, if we know the area and the base, by using the formula \\(h=\\frac{2A}{b}\\).<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1168345199361\" class=\"try\" data-type=\"note\">\r\n<div data-type=\"exercise\">\r\n<div id=\"fs-id1168345287977\" data-type=\"problem\">\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 4.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1168345389373\" data-type=\"problem\">\r\n<p id=\"fs-id1168341852742\">Use the formula \\(A=\\frac{1}{2}bh\\) to solve for \\(h\\):<\/p>\r\n<p id=\"fs-id1168345262141\">a) when \\(A=170\\) and \\(b=17\\) b) in general<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1168345277861\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\r\n<p id=\"fs-id1168345219463\">a) \\(h=20\\) b) \\(h=\\frac{2A}{b}\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 4.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1168345202847\" data-type=\"problem\">\r\n<p id=\"fs-id1168345559956\">Use the formula \\(A=\\frac{1}{2}bh\\) to solve for \\(b\\):<\/p>\r\n<p id=\"fs-id1168345213687\">a) when \\(A=62\\) and \\(h=31\\) b) in general<\/p>\r\n\r\n<\/div>\r\n<div data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\r\n<p id=\"fs-id1168345540818\">a) \\(b=4\\) b) \\(b=\\frac{2A}{h}\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1168345453615\">The formula \\(I=Prt\\) is used to calculate simple interest, <em data-effect=\"italics\">I<\/em>, for a principal, <em data-effect=\"italics\">P<\/em>, invested at rate, <em data-effect=\"italics\">r<\/em>, for <em data-effect=\"italics\">t<\/em> years.<\/p>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 5<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1168345291298\" data-type=\"problem\">\r\n<p id=\"fs-id1168345441444\">Solve the formula \\(I=Prt\\) to find the principal, \\(P\\):<\/p>\r\n<p class=\"p1\"><span class=\"s1\">a)<\/span> when \\(I=\\$5,600\\), \\(r=4\\%\\), \\(t=7\\phantom{\\rule{0.2em}{0ex}}years\\phantom{\\rule{0.2em}{0ex}}\\) <span class=\"s1\">b)<\/span> in general<\/p>\r\n\r\n<\/div>\r\n<div data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<table id=\"eip-id1168463859179\" style=\"width: 100%\" summary=\"This figure is a table that has seven rows and four columns. It shows the written instructions and the math for solving a formula when specific values are given, and for solving the formula in general. The first row, which is a header row, has only two cells: one that spans the first two columns, and one that spans the third and fourth columns. In the header row, the first cell to the left reads: \u201c(a) I equals 5,600 dollars, r equals 4 percent, t equals 7 years.\u201d The second cell reads: \u201c(b) in general.\u201d Below the header row, the first and third columns contain written instructions, and the second and fourth columns show math. In the second row, the first cell reads: \u201cWrite the formula.\u201d The second cell contains the equation I equals P times r times t. The third cell reads: \u201cWrite the formula.\u201d The fourth cell contains the equation I equals P times r times t. In the third row, the first cell to the left reads: \u201cSubstitute.\u201d The second cell contains the equation 5600 equals P times 0.04 times 7. The third and fourth cells are left blank. In the fourth row, the first cell to the left reads: \u201cSimplify.\u201d The second cell contains the equation 5600 equals P times 0.28. The third cell reads: \u201cSimplify.\u201d The fourth cell contains the equation I equals P times the product rt, with r times t written in parentheses. In the fifth row, the first cell to the left reads: \u201cDivide, to isolate P.\u201d The second cell contains the equation 5600 over 0.28 equals the product P times 0.28 over 0.28, with \u201cdivided by 0.28\u201d written in red on both sides. The third cell reads: \u201cDivide, to isolate P.\u201d The fourth cell contains the equation I over the product rt equals the product P times rt, with r times t in parentheses, over the product rt, with divided by the product rt\u201d written in red on both sides. In the sixth row, the first cell to the left reads: \u201cSimplify.\u201d The second cell contains the solution to the equation: 20,000 equals P. The third cell reads: \u201cSimplify.\u201d The fourth cell contains the solution to the equation: I over the product rt equals P. In the last row, the first cell to the left reads: \u201cThe principal is\u201d. The second cell contains the answer 20,000 dollars. The third cell is blank. The fourth cell contains the equation P equals I over the product r t.\" data-label=\"\">\r\n<tbody>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 47.5%;height: 14px\" colspan=\"2\">a)\\(I=\\$5,600\\), \\(r=4\\%\\), \\(t=7 years\\)<\/td>\r\n<td style=\"width: 47.6137%;height: 14px\" colspan=\"2\">b) in general<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 21.8182%;height: 14px\">Write the formula.<\/td>\r\n<td style=\"width: 25.6818%;height: 14px\">[latex]I = Prt[\/latex]<\/td>\r\n<td style=\"width: 21.8182%;height: 14px\">Write the formula.<\/td>\r\n<td style=\"width: 25.7955%;height: 14px\">[latex]I=Prt[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 21.8182%;height: 16px\">Substitute.<\/td>\r\n<td style=\"width: 25.6818%;height: 16px\">[latex]5600 = P(0.04)(7)[\/latex]<\/td>\r\n<td style=\"width: 21.8182%;height: 16px\"><\/td>\r\n<td style=\"width: 25.7955%;height: 16px\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 21.8182%;height: 16px\">Simplify.<\/td>\r\n<td style=\"width: 25.6818%;height: 16px\">[latex]5600=P(0.28)[\/latex]<\/td>\r\n<td style=\"width: 21.8182%;height: 16px\">Simplify.<\/td>\r\n<td style=\"width: 25.7955%;height: 16px\">[latex]I = P (rt)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Divide, to isolate <em data-effect=\"italics\">P<\/em>.<\/td>\r\n<td>[latex]\\frac{5600}{\\textcolor{red}{0.28}}=\\frac{P(0.28)}{\\textcolor{red}{0.28}}[\/latex]<\/td>\r\n<td>Divide, to isolate <em data-effect=\"italics\">P<\/em>.<\/td>\r\n<td>[latex]\\frac{I}{\\textcolor{red}{rt}}=\\frac{P(rt)}{\\textcolor{red}{rt}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 35px\">\r\n<td style=\"width: 21.8182%;height: 35px\">Simplify.<\/td>\r\n<td style=\"width: 25.6818%;height: 35px\">[latex]20,000 = P[\/latex]<\/td>\r\n<td style=\"width: 21.8182%;height: 35px\">Simplify.<\/td>\r\n<td style=\"width: 25.7955%;height: 35px\">[latex]\\frac{I}{rt}=P[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 36px\">\r\n<td style=\"width: 21.8182%;height: 36px\">The principal is<\/td>\r\n<td style=\"width: 25.6818%;height: 36px\">$[latex]20,000[\/latex]<\/td>\r\n<td style=\"width: 21.8182%;height: 36px\"><\/td>\r\n<td style=\"width: 25.7955%;height: 36px\">[latex]P=\\frac{I}{rt}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 5.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1168342181314\" data-type=\"problem\">\r\n<p id=\"fs-id1168345638820\">Use the formula \\(I=Prt\\) to find the principal, \\(P\\):<\/p>\r\n<p id=\"fs-id1168341889957\">a) when \\(I=\\$2,160\\), \\(r=6\\%\\), \\(t=3\\phantom{\\rule{0.2em}{0ex}}years\\phantom{\\rule{0.2em}{0ex}}\\) b) in general<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1168345669118\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\r\n<p id=\"fs-id1168345745251\">a) \\$12,000 b) \\(P=\\frac{I}{rt}\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 5.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div data-type=\"problem\">\r\n<p id=\"fs-id1168345445798\">Use the formula \\(I=Prt\\) to find the principal,\\(P\\):<\/p>\r\n<p id=\"fs-id1168345678089\">a) when \\(I=\\$5,400\\), \\(r=12\\%\\), \\(t=5\\phantom{\\rule{0.2em}{0ex}}years\\phantom{\\rule{0.2em}{0ex}}\\) b) in general<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1168341906686\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\r\n<p id=\"fs-id1168345398353\">a) $9,000 b) \\(P=\\frac{I}{rt}\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1168345486708\">Later in this class, and in future algebra classes, you\u2019ll encounter equations that relate two variables, usually <em data-effect=\"italics\">x<\/em> and <em data-effect=\"italics\">y<\/em>. You might be given an equation that is solved for <em data-effect=\"italics\">y<\/em> and need to solve it for <em data-effect=\"italics\">x<\/em>, or vice versa. In the following example, we\u2019re given an equation with both <em data-effect=\"italics\">x<\/em> and <em data-effect=\"italics\">y<\/em> on the same side and we\u2019ll solve it for <em data-effect=\"italics\">y<\/em>.<\/p>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 6<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1168345229876\" data-type=\"problem\">\r\n<p id=\"fs-id1168345229878\">Solve the formula \\(3x+2y=18\\) for <em data-effect=\"italics\">y<\/em>:<\/p>\r\n<p id=\"fs-id1168345427096\">a) when \\(x=4\\) b) in general<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1168341917214\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<table id=\"eip-id1168463888057\" style=\"width: 100%\" summary=\"This figure is a table that has seven rows and four columns. It shows the written instructions and the math for solving a formula when specific values are given, and for solving the formula in general. The first row, which is a header row, has only two cells: one that spans the first two columns, and one that spans the third and fourth columns. In the header row, the first cell to the left reads: \u201c(a) when x equals 4\u201d The second cell reads: \u201c(b) in general.\u201d Below the header row, the first and third columns contain written instructions, and the second and fourth columns show math. In the second row, the first cell is left blank. The second cell contains the equation 3 x plus 2 y equals 18. The third cell is left blank. The fourth cell contains the equation 3 x plus 2 y equals 18. In the third row, the first cell to the left reads: \u201cSubstitute.\u201d The second cell contains the equation 3 times 4 plus 2 y equals 18. The third and fourth cells are left blank. In the fourth row, the first cell to the left reads: \u201cSubtract to isolate the y-term.\u201d The second cell contains the equation 12 minus 12 plus 2 y equals 18 minus 12, with \u201cminus 12\u201d written in red on both sides. The third cell reads: \u201cSubtract to isolate the y-term.\u201d The fourth cell contains the equation 3 x minus 3 x plus 2 y equals 18 minus 3 x, with \u201cminus 3x\u201d written in red on both sides. In the fifth row, the first cell to the left reads: \u201cDivide.\u201d The second cell contains the equation the product 2 y over 2 equals 6 over 2, with \u201cdivided by 2\u201d written in red on both sides. The third cell reads: \u201cDivide.\u201d The fourth cell contains the equation the product 2 y over 2 equals 18 over 2 minus the product 3x over 2, with \u201cdivide by 2\u201d written in red for each term. In the last row, the first cell to the left reads: \u201cSimplify.\u201d The second cell contains the solution to the equation: y equals 3. The third cell reads: \u201cSimplify.\u201d The fourth cell contains the solution to the equation: y equals negative product 3 x over 2 plus 9.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 50.2273%\" colspan=\"2\">a) when \\(x=4\\)<\/td>\r\n<td style=\"width: 49.6591%\" colspan=\"2\">b) in general<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 21.25%\"><\/td>\r\n<td style=\"width: 28.9773%\">[latex]3x+2y=18[\/latex]<\/td>\r\n<td style=\"width: 21.25%\"><\/td>\r\n<td style=\"width: 28.4091%\">[latex]3x+2y=18[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 21.25%\">Substitute.<\/td>\r\n<td style=\"width: 28.9773%\"><span id=\"eip-id1168463876160\" data-type=\"media\" data-alt=\".\">[latex]3(\\textcolor{red}{4})+2y=18[\/latex]<\/span><\/td>\r\n<td style=\"width: 21.25%\"><\/td>\r\n<td style=\"width: 28.4091%\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 21.25%\">Subtract to isolate the\r\n\\(y\\)-term.<\/td>\r\n<td style=\"width: 28.9773%\">[latex]\\begin{gathered} 12\\textcolor{red}{-12}+2y=18\\textcolor{red}{-12}\\\\ 2y=6\\\\ \\end{gathered}[\/latex]<\/td>\r\n<td style=\"width: 21.25%\">Subtract to isolate the\r\n\\(y\\)-term.<\/td>\r\n<td style=\"width: 28.4091%\">[latex]\\begin{gathered} 3x\\textcolor{red}{-3x}+2y=18\\textcolor{red}{-3x}\\\\ 2y=18-3x\\\\ \\end{gathered}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 21.25%\">Divide.<\/td>\r\n<td style=\"width: 28.9773%\">[latex]\\frac{2y}{\\textcolor{red}{2}}=\\frac{6}{\\textcolor{red}{2}}[\/latex]<\/td>\r\n<td style=\"width: 21.25%\">Divide.<\/td>\r\n<td style=\"width: 28.4091%\">[latex]\\frac{2y}{\\textcolor{red}{2}}=\\frac{18}{\\textcolor{red}{2}}- \\frac{3x}{\\textcolor{red}{2}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 21.25%\">Simplify.<\/td>\r\n<td style=\"width: 28.9773%\">[latex]y=3[\/latex]<\/td>\r\n<td style=\"width: 21.25%\">Simplify.<\/td>\r\n<td style=\"width: 28.4091%\">[latex]y=9-\\frac{3}{2} x[\/latex]\r\nor\r\n[latex]y=-\\frac{3}{2} x+9[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 6.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1168341973908\" data-type=\"problem\">\r\n<p id=\"fs-id1168345445835\">Solve the formula \\(3x+4y=10\\) for <em data-effect=\"italics\">y<\/em>:<\/p>\r\n<p id=\"fs-id1168345572426\">a) when \\(x=\\frac{14}{3}\\) \u00a0\u00a0\u00a0 b) in general<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1168341960142\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\r\n<p id=\"fs-id1168345423533\">a)\\(y=-1\\) \u00a0\u00a0\u00a0 b)\\(y=\\frac{10-3x}{4}\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TY IT 6.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1168345558322\" data-type=\"problem\">\r\n<p id=\"fs-id1168345558324\">Solve the formula \\(5x+2y=18\\) for <em data-effect=\"italics\">y:<\/em><\/p>\r\n<p id=\"fs-id1168342046117\">a) when \\(x=4\\) \u00a0\u00a0\u00a0 b) in general<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1168342180725\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\r\n<p id=\"fs-id1168342180727\">a)\\(y=-1\\)\u00a0 \u00a0\u00a0\u00a0\u00a0 b)\\(y=\\frac{18-5x}{2}\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1169751859527\">Now we will solve a formula in general without using numbers as a guide.<\/p>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 7<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1168345385685\" data-type=\"problem\">\r\n<p id=\"fs-id1168345423448\">Solve the formula \\(P=a+b+c\\) for \\(a\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1168345456529\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<table id=\"eip-id1168463887699\" style=\"width: 100%\" summary=\"This figure is has two columns, with written instructions on the left and math on the right. At the top of the figure on the left, the instructions say: \u201cWe will isolate a on one side of the equation.\u201d To the right of this instruction is the original equation: P equals a plus b plus c. One line down on the left, the instructions say: \u201cBoth b and c are added to a, so we subtract them from both sides of the equation.\u201d To the right of this sentence is the original equation with b and c subtracted from both sides of the equation: P minus b minus c equals a plus b plus c minus b minus c, with \u201cminus b minus c\u201d written in red on both sides. Another line down on the left, the instructions say: \u201cSimplify.\u201d To the right of this instruction is the equation P minus b minus c equals a. Below this is the equation a equals P minus b minus c.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td>We will isolate \\(a\\) on one side of the equation.<\/td>\r\n<td>[latex]P=a+b+c[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Both \\(b\\) and \\(c\\) are added to \\(a\\), so we subtract them from both sides of the equation.<\/td>\r\n<td><span id=\"eip-id1168463887754\" data-type=\"media\" data-alt=\".\">[latex]P \\textcolor{red}{-b-c} = a+b+c \\textcolor{red}{-b-c}[\/latex]<\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]\\begin{gathered} P-b-c=a \\\\ \\text{or} \\\\ a=P-b-c \\end{gathered}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1168345539191\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1168345539194\" data-type=\"exercise\">\r\n<div id=\"fs-id1168345539196\" data-type=\"problem\">\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 7.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nSolve the formula \\(P=a+b+c\\) for <em>b<\/em>.\r\n<div id=\"fs-id1168345622774\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\r\n<p id=\"fs-id1168345622777\">\\(b=P-a-c\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 7.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1168345543450\" data-type=\"problem\">\r\n<p id=\"fs-id1168345543452\">Solve the formula \\(P=a+b+c\\) for <em data-effect=\"italics\">c<\/em>.<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1168341906957\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\r\n<p id=\"fs-id1168341906959\">\\(c=P-a-b\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1168345543445\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1168345543448\" data-type=\"exercise\">\r\n<div id=\"fs-id1168341906957\" data-type=\"solution\">\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 8<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1168345621361\" data-type=\"problem\">\r\n<p id=\"fs-id1168345621363\">Solve the formula \\(6x+5y=13\\) for <em data-effect=\"italics\">y.<\/em><\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1168345525269\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<table id=\"eip-id1168462677762\" style=\"width: 100%\" summary=\"This figure has two columns, with written instructions on the left and math on the right. At the top of the figure on the right is the equation 6x plus 5 y equals 13. One line down on the left, the instructions say: \u201cSubtract 6 x from both sides to isolate the term with y. To the right of this sentence is the original equation with 6x subtracted from both sides: 6 x minus 6 x plus 5y equals 13 minus 6x, with \u201cminus 6 x\u201d written in red on both sides. Another line down on the left, the instructions say: \u201cSimplify.\u201d To the right of this word is the equation 5y equals 13 minus 6 x. One more line down on the left, the instructions say: \u201cDivide by 5 to make the coefficient 1.\u201d To the right of this instruction is the equation with both sides divided by 5: 5y over 5 equals the difference 13 minus 6 x over 5, with \u201cdivided by 5\u201d written in red on both sides. One more line down on the left, the instructions say: \u201cSimplify.\u201d To the right of this word is the equation y equals the difference 13 minus 6 x over 5.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]6x+5y=13[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Subtract \\(6x\\) from both sides to isolate the term with \\(y\\).<\/td>\r\n<td>[latex]6x \\textcolor{red}{-6x} +5y = 13 \\textcolor{red}{-6x}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]5y=13-6x[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Divide by 5 to make the coefficient 1.<\/td>\r\n<td>[latex]\\frac{5y}{\\textcolor{red}{5}}=\\frac{13-6x}{\\textcolor{red}{5}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]y=\\frac{13-6x}{5}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p id=\"fs-id1168342104215\">The fraction is simplified. We cannot divide \\(13-6x\\) by 5<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1168342168215\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1168342168219\" data-type=\"exercise\">\r\n<div id=\"fs-id1168342168221\" data-type=\"problem\">\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 8.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1168342168221\" data-type=\"problem\">\r\n<p id=\"fs-id1168342168223\">Solve the formula \\(4x+7y=9\\) for <em data-effect=\"italics\">y.<\/em><\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1168345621178\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\r\n<p id=\"fs-id1168345621180\">\\(y=\\frac{9-4x}{7}\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 8.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1168345542275\" data-type=\"problem\">\r\n<p id=\"fs-id1168345542278\">Solve the formula \\(5x+8y=1\\) for <em data-effect=\"italics\">y.<\/em><\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1168345424572\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\r\n<p id=\"fs-id1168345424574\">\\(y=\\frac{1-5x}{8}\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<h1 data-type=\"title\">Key Concepts<\/h1>\r\n<ul id=\"fs-id1168345670000\" data-bullet-style=\"bullet\">\r\n \t<li><strong data-effect=\"bold\">To Solve an Application (with a formula)<\/strong>\r\n<ol id=\"fs-id1168345670010\" class=\"stepwise\" type=\"1\">\r\n \t<li><strong data-effect=\"bold\">Read<\/strong> the problem. Make sure all the words and ideas are understood.<\/li>\r\n \t<li><strong data-effect=\"bold\">Identify<\/strong> what we are looking for.<\/li>\r\n \t<li><strong data-effect=\"bold\">Name<\/strong> what we are looking for. Choose a variable to represent that quantity.<\/li>\r\n \t<li><strong data-effect=\"bold\">Translate<\/strong> into an equation. Write the appropriate formula for the situation. Substitute in the given information.<\/li>\r\n \t<li><strong data-effect=\"bold\">Solve<\/strong> the equation using good algebra techniques.<\/li>\r\n \t<li><strong data-effect=\"bold\">Check<\/strong> the answer in the problem and make sure it makes sense.<\/li>\r\n \t<li><strong data-effect=\"bold\">Answer<\/strong> the question with a complete sentence.<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li><strong data-effect=\"bold\">Distance, Rate and Time<\/strong>\r\nFor an object moving at a uniform (constant) rate, the distance traveled, the elapsed time, and the rate are related by the formula: \\(d=rt\\) where <em data-effect=\"italics\">d<\/em> = distance, <em data-effect=\"italics\">r<\/em> = rate, <em data-effect=\"italics\">t<\/em> = time.<\/li>\r\n \t<li><strong data-effect=\"bold\">To solve a formula for a specific variable<\/strong> means to get that variable by itself with a coefficient of 1 on one side of the equation and all other variables and constants on the other side.<\/li>\r\n<\/ul>\r\n<h1 data-type=\"title\">Practice Makes Perfect<\/h1>\r\n<h2 id=\"fs-id1168345726412\">Use the Distance, Rate, and Time Formula<\/h2>\r\n<p id=\"fs-id1169754187572\">In the following exercises, solve.<\/p>\r\n\r\n<table style=\"border-collapse: collapse;width: 100%;height: 352px\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 51.3711%\">1. Socorro drove for \\(4\\frac{5}{6}\\) hours at 60 miles per hour. How much distance did she travel?<\/td>\r\n<td style=\"width: 48.6289%\">2. Steve drove for \\(8\\frac{1}{2}\\) hours at 72 miles per hour. How much distance did he travel?<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 51.3711%\">3. Francie rode her bike for \\(2\\frac{1}{2}\\) hours at 12 miles per hour. How far did she ride?<\/td>\r\n<td style=\"width: 48.6289%\">4. Yuki walked for \\(1\\frac{3}{4}\\) hours at 4 miles per hour. How far did she walk?<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 51.3711%\">5. Marta is taking the bus from Abbotsford to Cranbrook. The distance is 774 km and the bus travels at a steady rate of 86 miles per hour. How long will the bus ride be?<\/td>\r\n<td style=\"width: 48.6289%\">6. Connor wants to drive from Vancouver to the Nakusp, a distance of 630 km. If he drives at a steady rate of 90 km\/h, how many hours will the trip take?<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 51.3711%\">7. Kareem wants to ride his bike from Golden, BC to Banff, AB. The distance is 140 km. If he rides at a steady rate of 20 km\/h, how many hours will the trip take?<\/td>\r\n<td style=\"width: 48.6289%\">8. Aurelia is driving from Calgary to Edmonton at a rate of 85 km\/h. The distance is 300 km. To the nearest tenth of an hour, how long will the trip take?<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 51.3711%\">9. Alejandra is driving to Prince George, 450 km away. If she wants to be there in 6 hours, at what rate does she need to drive?<\/td>\r\n<td style=\"width: 48.6289%\">10. Javier is driving to Vernon, 240 km away. If he needs to be in Vernon in 3 hours, at what rate does he need to drive?<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 51.3711%\">11. Philip got a ride with a friend from Calgary to Kelowna, a distance of 890 km. If the trip took 10 hours, how fast was the friend driving?<\/td>\r\n<td style=\"width: 48.6289%\">12. Aisha took the train from Spokane to Seattle. The distance is 280 miles and the trip took 3.5 hours. What was the speed of the train?<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<h2 id=\"fs-id1168345688676\">Solve a Formula for a Specific Variable<\/h2>\r\n<table border=\"0\">\r\n<tbody>\r\n<tr>\r\n<td>13. Solve for \\(t\\) using \\(d=rt\\)\r\n<ol style=\"list-style-type: lower-alpha\">\r\n \t<li>when \\(d=240\\phantom{\\rule{0.2em}{0ex}}\\text{and}\\phantom{\\rule{0.2em}{0ex}}r=60\\)<\/li>\r\n \t<li>in general<\/li>\r\n<\/ol>\r\n<\/td>\r\n<td>14. Solve for \\(t\\) using \\(d=rt\\)\r\n<ol style=\"list-style-type: lower-alpha\">\r\n \t<li>when \\(d=350\\) and \\(r=70\\)<\/li>\r\n \t<li>in general<\/li>\r\n<\/ol>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>15. Solve for \\(t\\) using \\(d=rt\\)\r\n<ol style=\"list-style-type: lower-alpha\">\r\n \t<li>when \\(d=175\\phantom{\\rule{0.2em}{0ex}}\\text{and}\\phantom{\\rule{0.2em}{0ex}}r=50\\)<\/li>\r\n \t<li>in general<\/li>\r\n<\/ol>\r\n<\/td>\r\n<td>16. Solve for \\(t\\) using \\(d=rt\\)\r\n<ol style=\"list-style-type: lower-alpha\">\r\n \t<li>when \\(d=510\\phantom{\\rule{0.2em}{0ex}}\\text{and}\\phantom{\\rule{0.2em}{0ex}}r=60\\)<\/li>\r\n \t<li>in general<\/li>\r\n<\/ol>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>17. Solve for \\(r\\) using \\(d=rt\\)\r\n<ol style=\"list-style-type: lower-alpha\">\r\n \t<li>when \\(d=420\\phantom{\\rule{0.2em}{0ex}}\\text{and}\\phantom{\\rule{0.2em}{0ex}}t=6\\)<\/li>\r\n \t<li>in general<\/li>\r\n<\/ol>\r\n<\/td>\r\n<td>18. Solve for \\(r\\) using\u00a0\\(d=rt\\)\r\n<ol style=\"list-style-type: lower-alpha\">\r\n \t<li>when \\(d=204\\phantom{\\rule{0.2em}{0ex}}\\text{and}\\phantom{\\rule{0.2em}{0ex}}t=3\\)<\/li>\r\n \t<li>in general<\/li>\r\n<\/ol>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>\r\n<div data-type=\"exercise\">\r\n<div data-type=\"problem\">\r\n\r\n19. Solve for \\(r\\) using\u00a0\\(d=rt\\)\r\n<ol style=\"list-style-type: lower-alpha\">\r\n \t<li>when \\(d=180\\phantom{\\rule{0.2em}{0ex}}\\text{and}\\phantom{\\rule{0.2em}{0ex}}t=4.5\\)<\/li>\r\n \t<li>in general<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div><\/td>\r\n<td>20. Solve for \\(r\\) using\u00a0\\(d=rt\\)\r\n<ol style=\"list-style-type: lower-alpha\">\r\n \t<li>when \\(d=160\\phantom{\\rule{0.2em}{0ex}}\\text{and}\\phantom{\\rule{0.2em}{0ex}}t=2.5\\)<\/li>\r\n \t<li>in general<\/li>\r\n<\/ol>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>21. Solve for \\(h\\) using \\(A=\\frac{1}{2}bh\\)\r\n<ol style=\"list-style-type: lower-alpha\">\r\n \t<li>when \\(A=176\\phantom{\\rule{0.2em}{0ex}}\\text{and}\\phantom{\\rule{0.2em}{0ex}}b=22\\)<\/li>\r\n \t<li>in general<\/li>\r\n<\/ol>\r\n<\/td>\r\n<td>22. Solve for \\(b\\) using \\(A=\\frac{1}{2}bh\\)\r\n<ol style=\"list-style-type: lower-alpha\">\r\n \t<li>when \\(A=126\\phantom{\\rule{0.2em}{0ex}}\\text{and}\\phantom{\\rule{0.2em}{0ex}}h=18\\)<\/li>\r\n \t<li>in general<\/li>\r\n<\/ol>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>23. Solve for the principal, P using \\(I = Prt\\)\u00a0 for\r\n<ol style=\"list-style-type: lower-alpha\">\r\n \t<li>\\(I=\\$5,480\\),\\(r=4\\%\\),\\(t=7\\phantom{\\rule{0.2em}{0ex}}\\text{years}\\phantom{\\rule{0.2em}{0ex}}\\)<\/li>\r\n \t<li>in general<\/li>\r\n<\/ol>\r\n<\/td>\r\n<td>\r\n<div data-type=\"exercise\">\r\n<div data-type=\"problem\">24. Solve for \\(b\\) using \\(A=\\frac{1}{2}bh\\)<\/div>\r\n<ol style=\"list-style-type: lower-alpha\">\r\n \t<li data-type=\"problem\">when \\(A=65\\phantom{\\rule{0.2em}{0ex}}\\text{and}\\phantom{\\rule{0.2em}{0ex}}h=13\\)<\/li>\r\n \t<li data-type=\"problem\">in general.<\/li>\r\n<\/ol>\r\n<\/div><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>25. Solve for the time, t\u00a0 using \\(I = Prt\\) for\r\n<ol style=\"list-style-type: lower-alpha\">\r\n \t<li>\\(I=\\$2,376\\),\\(P=\\$9,000\\) ,\\(r=4.4\\%\\)<\/li>\r\n \t<li>in general<\/li>\r\n<\/ol>\r\n<\/td>\r\n<td>26. Solve for the principal, P using \\(I = Prt\\) for\r\n<ol style=\"list-style-type: lower-alpha\">\r\n \t<li>\\(I=\\$3,950\\),\\(r=6\\%\\),\\(t=5\\phantom{\\rule{0.2em}{0ex}}\\text{years}\\phantom{\\rule{0.2em}{0ex}}\\)<\/li>\r\n \t<li>in general<\/li>\r\n<\/ol>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>27. Solve the formula \\(2x+3y=12\\) for y when\r\n<ol style=\"list-style-type: lower-alpha\">\r\n \t<li>\\(x=3\\)<\/li>\r\n \t<li>in general<\/li>\r\n<\/ol>\r\n<\/td>\r\n<td>\r\n<div data-type=\"exercise\">\r\n<div data-type=\"problem\">28. Solve for the time, t for<\/div>\r\n<ol style=\"list-style-type: lower-alpha\">\r\n \t<li data-type=\"problem\">\\(I=\\$624\\),\\(P=\\$6,000\\),\\(r=5.2\\%\\)<\/li>\r\n \t<li data-type=\"problem\">in general<\/li>\r\n<\/ol>\r\n<\/div><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>29. Solve the formula \\(3x-y=7\\) for y when\r\n<ol style=\"list-style-type: lower-alpha\">\r\n \t<li>\\(x=-2\\)<\/li>\r\n \t<li>in general<\/li>\r\n<\/ol>\r\n<\/td>\r\n<td>30. Solve the formula \\(5x+2y=10\\) for y when\r\n<ol style=\"list-style-type: lower-alpha\">\r\n \t<li>\\(x=4\\)<\/li>\r\n \t<li>in general<\/li>\r\n<\/ol>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>31. Solve \\(a+b=90\\) for\r\n<ol style=\"list-style-type: lower-alpha\">\r\n \t<li>[latex]a[\/latex] when [latex]b = 50[\/latex]<\/li>\r\n \t<li>\\(a\\) in general<\/li>\r\n<\/ol>\r\n<\/td>\r\n<td>32. Solve the formula \\(4x+y=5\\) for y when\r\n<ol style=\"list-style-type: lower-alpha\">\r\n \t<li>\\(x=-3\\)<\/li>\r\n \t<li>in general<\/li>\r\n<\/ol>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>33. Solve \\(180=a+b+c\\) for \\(a\\).<\/td>\r\n<td>34. Solve \\(a+b=90\\) for \\(a\\).<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>35. Solve the formula \\(8x+y=15\\) for y.<\/td>\r\n<td>36. Solve \\(180=a+b+c\\) for \\(c\\).<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>37. Solve the formula \\(-4x+y=-6\\) for y.<\/td>\r\n<td>38. Solve the formula \\(9x+y=13\\) for y.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>39. Solve the formula \\(4x+3y=7\\) for y.<\/td>\r\n<td>40. Solve the formula \\(-5x+y=-1\\) for y.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>41. Solve the formula \\(x-y=-4\\) for y.<\/td>\r\n<td>42. Solve the formula \\(3x+2y=11\\) for y.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>43. Solve the formula \\(P=2L+2W\\) for \\(L\\).<\/td>\r\n<td>44. Solve the formula \\(x-y=-3\\) for y.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>45. Solve the formula \\(C=\\pi d\\) for \\(d\\).<\/td>\r\n<td>46. Solve the formula \\(P=2L+2W\\) for \\(W\\).<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>47. Solve the formula \\(V=LWH\\) for \\(L\\).<\/td>\r\n<td>48. Solve the formula \\(C=\\pi d\\) for \\(\\pi \\).<\/td>\r\n<\/tr>\r\n<tr>\r\n<td colspan=\"2\">49. Solve the formula \\(V=LWH\\) for \\(H\\).<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<h3 data-type=\"title\">Everyday Math<\/h3>\r\n<table style=\"border-collapse: collapse;width: 100%\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 51.0055%\">50.<strong data-effect=\"bold\"> Converting temperature.<\/strong> Yon was visiting the United States and he saw that the temperature in Seattle one day was 50<sup>o<\/sup> Fahrenheit. Solve for C in the formula \\(F=\\frac{9}{5}C+32\\) to find the Celsius temperature.<\/td>\r\n<td style=\"width: 48.9945%\">51.<strong data-effect=\"bold\"> Converting temperature.<\/strong> While on a tour in Greece, Tatyana saw that the temperature was 40<sup>o<\/sup> Celsius. Solve for F in the formula \\(C=\\frac{5}{9}\\left(F-32\\right)\\) to find the Fahrenheit temperature.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<h3 data-type=\"title\">Writing Exercises<\/h3>\r\n<div id=\"fs-id1168345741424\" data-type=\"exercise\">\r\n<div id=\"fs-id1168345741426\" data-type=\"problem\">\r\n<table style=\"border-collapse: collapse;width: 100%\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 50.0914%\">52. Solve the equation \\(5x-2y=10\\) for \\(x\\)\r\na) when \\(y=10\\)\r\nb) in general\r\nc) Which solution is easier for you, a) or b)? Why?<\/td>\r\n<td style=\"width: 49.9086%\">53. Solve the equation \\(2x+3y=6\\) for \\(y\\)\r\na) when \\(x=-3\\)\r\nb) in general\r\nc) Which solution is easier for you, a) or b)? Why?<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<h1>Answers<\/h1>\r\n<table style=\"width: 100%\">\r\n<tbody>\r\n<tr>\r\n<td>1. 290 miles<\/td>\r\n<td>3. 30 miles<\/td>\r\n<td>5. 9 hr<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>7. 7 hr<\/td>\r\n<td>9. 75 km\/hr<\/td>\r\n<td>11. 89 km\/hr<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>13.\r\n<ol type=\"a\">\r\n \t<li>[latex]t=4[\/latex]<\/li>\r\n \t<li>\\(t=\\frac{d}{r}\\)<\/li>\r\n<\/ol>\r\n<\/td>\r\n<td>15.\r\n<ol type=\"a\">\r\n \t<li>[latex]t= 3.5[\/latex]<\/li>\r\n \t<li>\\(t=\\frac{d}{r}\\)<\/li>\r\n<\/ol>\r\n<\/td>\r\n<td>17.\r\n<ol type=\"a\">\r\n \t<li>[latex] r= 70[\/latex]<\/li>\r\n \t<li>\\(r=\\frac{d}{t}\\)<\/li>\r\n<\/ol>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>19.\r\n<ol style=\"list-style-type: lower-alpha\">\r\n \t<li>[latex]r= 40[\/latex]<\/li>\r\n \t<li>\\(r=\\frac{d}{t}\\)<\/li>\r\n<\/ol>\r\n<\/td>\r\n<td>21.\r\n<ol style=\"list-style-type: lower-alpha\">\r\n \t<li>[latex] h= 16[\/latex]<\/li>\r\n \t<li>\\(h=\\frac{2A}{b}\\)<\/li>\r\n<\/ol>\r\n<\/td>\r\n<td>23.\r\n<ol style=\"list-style-type: lower-alpha\">\r\n \t<li>\\(P= \\$19,571.43\\)<\/li>\r\n \t<li>\\(P=\\frac{I}{rt}\\)<\/li>\r\n<\/ol>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>25.\r\n<ol style=\"list-style-type: lower-alpha\">\r\n \t<li>[latex]t= 6[\/latex]<\/li>\r\n \t<li>\\(t=\\frac{I}{Pr}\\)<\/li>\r\n<\/ol>\r\n<\/td>\r\n<td>27.\r\n<ol style=\"list-style-type: lower-alpha\">\r\n \t<li>[latex] y=2 [\/latex]<\/li>\r\n \t<li>\\(y=\\frac{12-2x}{3}\\)<\/li>\r\n<\/ol>\r\n<\/td>\r\n<td>29.\r\n<ol style=\"list-style-type: lower-alpha\">\r\n \t<li>[latex] y= -13[\/latex]<\/li>\r\n \t<li>\\(y=-7+3x\\) or \\(y=3x-7\\)<\/li>\r\n<\/ol>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>31. [latex]40[\/latex]; [latex]a= 90-b[\/latex]<\/td>\r\n<td>33. [latex]a= 180-b-c[\/latex]<\/td>\r\n<td>35. [latex]y= 15-8x[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>37. [latex]y= 4x-6[\/latex]<\/td>\r\n<td>39. [latex]y= \\frac{7-4x}{3}[\/latex]<\/td>\r\n<td>41. [latex]y= 4+x[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>43. [latex] L= \\frac{P-2W}{2}[\/latex]<\/td>\r\n<td>45. [latex]d= \\frac{C}{\\pi}[\/latex]<\/td>\r\n<td>47. [latex] L= \\frac{V}{WH}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>49. [latex]H= \\frac{V}{LW}[\/latex]<\/td>\r\n<td>51. \\(F= 104\\)<sup>o<\/sup><\/td>\r\n<td>53. Answers will vary<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<h1>Attributions<\/h1>\r\nThis chapter has been adapted from \u201cSolve a Formula for a Specific Variable\u201d in <a href=\"https:\/\/openstax.org\/details\/books\/elementary-algebra\"><em>Elementary Algebra<\/em> (OpenStax)<\/a> by Lynn Marecek and MaryAnne Anthony-Smith, which is under a <a href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY 4.0 Licence<\/a>. Adapted by Izabela Mazur. See the Copyright page for more information.","rendered":"<div class=\"textbox textbox--learning-objectives\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Learning Objectives<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>By the end of this section, you will be able to:<\/p>\n<ul>\n<li>Use the Distance, Rate, and Time formula<\/li>\n<li>Solve a formula for a specific variable<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<h1 data-type=\"title\">Use the Distance, Rate, and Time Formula<\/h1>\n<p id=\"fs-id1168342181224\">One formula you will use often in algebra and in everyday life is the formula for distance traveled by an object moving at a constant rate. Rate is an equivalent word for \u201cspeed.\u201d The basic idea of rate may already be familiar to you. Do you know what distance you travel if you drive at a steady rate of 60 miles per hour for 2 hours? (This might happen if you use your car\u2019s cruise control while driving on the highway.) If you said 120 miles, you already know how to use this formula!<\/p>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Distance, Rate, and Time<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1168345633583\">For an object moving at a uniform (constant) rate, the distance traveled, the elapsed time, and the rate are related by the formula:<\/p>\n<div id=\"fs-id1166502309552\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-02e77a82ef7700a52287327929a43228_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;&#125;&#100;&#61;&#114;&#116;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#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;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#100;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#100;&#105;&#115;&#116;&#97;&#110;&#99;&#101;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#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;&#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=\"56\" width=\"310\" style=\"vertical-align: -22px;\" \/><\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1168345636448\">We will use the Strategy for Solving Applications that we used earlier in this chapter. When our problem requires a formula, we change Step 4. In place of writing a sentence, we write the appropriate formula. We write the revised steps here for reference.<\/p>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">HOW TO: Solve an application (with a formula).<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<ol id=\"fs-id1169751874724\" class=\"stepwise\" type=\"1\">\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 we are looking for.<\/li>\n<li><strong data-effect=\"bold\">Name<\/strong> what we are looking for. Choose a variable to represent that quantity.<\/li>\n<li><strong data-effect=\"bold\">Translate<\/strong> into an equation. Write the appropriate formula for the situation. Substitute in the given information.<\/li>\n<li><strong data-effect=\"bold\">Solve<\/strong> the equation using good algebra techniques.<\/li>\n<li><strong data-effect=\"bold\">Check<\/strong> the answer in the problem and 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<p id=\"fs-id1168345529730\">You may want to create a mini-chart to summarize the information in the problem. See the chart in this first example.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345384975\" data-type=\"problem\">\n<p id=\"fs-id1168345276335\">Jamal rides his bike at a uniform rate of 12 miles per hour for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-5cb7e372608f573368e8eb31f878cc23_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"18\" style=\"vertical-align: -6px;\" \/> hours. What distance has he traveled?<\/p>\n<\/div>\n<div id=\"fs-id1168341892523\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"fs-id1167270960754\" class=\"unnumbered unstyled\" style=\"width: 100%\" summary=\"This figure is a table that has two columns and seven rows. The first column is a header column, and it contains the names and numbers of each step. The second column contains math answers. On the top row of the table, the first cell on the left reads: \u201cStep 1. Read the problem.\u201d In the second row of the table, the first cell on the left reads: \u201cStep 2. Identify what you are looking for.\u201d The second cell contains the answer \u201cdistance traveled\u201d. In the third row of the table, the first cell on the left reads: \u201cStep 3. Name: Choose a variable to represent it.\u201d The second cell contains the answer: \u201clet d equal distance\u201d. In the fourth row of the table, the first cell on the left reads: \u201cStep 4. Translate: Write the appropriate formula. Substitute in the given information.\u201d The second cell contains the formula d equals rt. Below this is a table with one column of three cells. From top to bottom, the cells reads: \u201cd equals ?\u201d, \u201cr equals 12 mph\u201d, and \u201ct equals 3 and one-half hours\u201d. Below this is the formula with the given information substituted in: d equals 12 times 3 and a half. In the fifth row of the table, the first cell on the left reads: \u201cStep 5. Solve the equation.\u201d The second cell contains the equation d equals 42 miles. In the sixth row of the table, the first cell on the left reads: \u201cStep 6. Check. Does 42 miles make sense? Jamal rides: 12 miles in 1 hour, 24 miles in 2 hours, 36 miles in 3 hours, 48 miles in 4 hours.\u201d There is an arrow pointing between 3 and 4 hours, and it indicates: \u201c42 miles in 3 and a half hours is reasonable.\u201d In the seventh row of the table, the first cell on the left reads: \u201cAnswer the question with a complete sentence.\u201d The second cell contains the sentence: \u201cJamal rode 42 miles.\" data-label=\"\">\n<tbody>\n<tr>\n<td><strong data-effect=\"bold\">Step 1. Read<\/strong> the problem.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><strong data-effect=\"bold\">Step 2. Identify<\/strong> what you are looking for.<\/td>\n<td>distance traveled<\/td>\n<\/tr>\n<tr>\n<td><strong data-effect=\"bold\">Step 3. Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>Let <em data-effect=\"italics\">d<\/em> = distance.<\/td>\n<\/tr>\n<tr>\n<td><strong data-effect=\"bold\">Step 4. Translate:<\/strong> Write the appropriate formula.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b3865773037202207382ec637cb61193_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#100;&#61;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"47\" style=\"vertical-align: 0px;\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-8956e1913a593d897156be5f45453637_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#100;&#61;&#63;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"36\" style=\"vertical-align: 0px;\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-152787cee2247480da3c24492cdf36f6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;&#61;&#49;&#50;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"49\" style=\"vertical-align: 0px;\" \/> mph<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2227b6ca5277f6179d0b0f1312e7e27c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#116;&#61;&#51;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"48\" style=\"vertical-align: -6px;\" \/> hours<\/td>\n<\/tr>\n<tr>\n<td>Substitute in the given information.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-1a7d7db835b434d853406de4f8751e44_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#100;&#61;&#49;&#50;&#92;&#99;&#100;&#111;&#116;&#32;&#51;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"81\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td><strong data-effect=\"bold\">Step 5. Solve<\/strong> the equation.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9613bb755ff2ab021b0a01e07fbfebdb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#100;&#61;&#52;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"50\" style=\"vertical-align: 0px;\" \/> miles<\/td>\n<\/tr>\n<tr>\n<td><strong data-effect=\"bold\">Step 6. Check<\/strong><\/p>\n<p>Does 42 miles make sense?<\/p>\n<p>Jamal rides:<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-7e547ad5cc9728c24aaaaa17838e0b3d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#92;&#49;&#50;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#32;&#109;&#105;&#108;&#101;&#115;&#32;&#105;&#110;&#32;&#125;&#32;&#49;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#32;&#104;&#111;&#117;&#114;&#125;&#92;&#92; &#50;&#52;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#109;&#105;&#108;&#101;&#115;&#32;&#105;&#110;&#32;&#125;&#32;&#50;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#32;&#104;&#111;&#117;&#114;&#115;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"34\" width=\"142\" style=\"vertical-align: 0px;\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d66065aeb355b271784966490a02a188_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#32;&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#32;&#92;&#113;&#117;&#97;&#100;&#38;&#92;&#108;&#101;&#102;&#116;&#92;&#32;&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#116;&#97;&#98;&#117;&#108;&#97;&#114;&#125;&#123;&#64;&#123;&#125;&#108;&#64;&#123;&#125;&#125;&#32;&#51;&#54;&#32;&#109;&#105;&#108;&#101;&#115;&#32;&#105;&#110;&#32;&#51;&#32;&#104;&#111;&#117;&#114;&#115;&#32;&#92;&#92;&#32;&#52;&#56;&#32;&#109;&#105;&#108;&#101;&#115;&#32;&#105;&#110;&#32;&#52;&#32;&#104;&#111;&#117;&#114;&#115;&#32;&#92;&#101;&#110;&#100;&#123;&#116;&#97;&#98;&#117;&#108;&#97;&#114;&#125;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#92;&#125;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#52;&#50;&#32;&#109;&#105;&#108;&#101;&#115;&#32;&#105;&#110;&#32;&#125;&#32;&#51;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#104;&#111;&#117;&#114;&#115;&#32;&#115;&#101;&#101;&#109;&#115;&#32;&#114;&#101;&#97;&#115;&#111;&#110;&#97;&#98;&#108;&#101;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"459\" style=\"vertical-align: -28px;\" \/><\/td>\n<\/tr>\n<tr>\n<td><strong data-effect=\"bold\">Step 7. Answer the question<\/strong> with a complete sentence.<\/td>\n<td>Jamal rode 42 miles.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168345418079\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168341907611\" data-type=\"exercise\">\n<div id=\"fs-id1168345302709\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345302709\" data-type=\"problem\">\n<p id=\"fs-id1168345691673\">Lindsay drove for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9964fcab73a4908be8886950459fc429_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"18\" style=\"vertical-align: -6px;\" \/> hours at 60 miles per hour. How much distance did she travel?<\/p>\n<\/div>\n<div id=\"fs-id1168345461727\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168345451606\">330 miles<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345557101\" data-type=\"problem\">\n<p id=\"fs-id1168345215800\">Trinh walked for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d6bcaecf460ec4637e44c0f8c6c5287f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"18\" style=\"vertical-align: -6px;\" \/> hours at 3 miles per hour. How far did she walk?<\/p>\n<\/div>\n<div id=\"fs-id1168345240061\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168345262359\">7 miles<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345454045\" data-type=\"problem\">\n<p id=\"fs-id1168345385591\">Rey is planning to drive from his house in Saskatoon to visit his grandmother in Winnipeg, a distance of 798 km. If he can drive at a steady rate of 76 km per hour, how many hours will the trip take?<\/p>\n<\/div>\n<div id=\"fs-id1168342180736\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"fs-id1167271046130\" style=\"width: 100%\" summary=\"This figure is a table that has two columns and seven rows. The first column is a header column, and it contains the names and numbers of each step. The second column contains math answers. On the top row of the table, the first cell on the left reads: \u201cStep 1. Read the problem.\u201d In the second row of the table, the first cell on the left reads: \u201cStep 2. Identify what you are looking for.\u201d The second cell contains the answer \u201chow many hours (time)\u201d. In the third row of the table, the first cell on the left reads: \u201cStep 3. Name: Choose a variable to represent it.\u201d The second cell contains the answer: \u201clet t equal time\u201d. Below this is a table with one column of three cells. From top to bottom, the cells reads: \u201cd equals 520 miles\u201d, \u201cr equals 65 mph\u201d, and \u201ct equals ? hours\u201d. In the fourth row of the table, the first cell on the left reads: \u201cStep 4. Translate: Write the appropriate formula. Substitute in the given information.\u201d The second cell contains the formula d equals rt. Below this is the formula with the given information substituted in: 520 equals 65t. In the fifth row of the table, the first cell on the left reads: \u201cStep 5. Solve the equation.\u201d The second cell contains the equation t equals 8. In the sixth row of the table, the first cell on the left reads: \u201cStep 6. Check. Substitute the numbers into the formula and make sure the result is a true statement.\u201d Below this is the equation d equals rt. Below this is the equation 520 might equal 65 times 8. Below this is the equation 520 equals 520, with a check mark next to it. In the seventh row of the table, the first cell on the left reads: \u201cAnswer the question with a complete sentence. Ray\u2019s trip will take 8 hours.\u201d\" data-label=\"\">\n<tbody>\n<tr>\n<td><strong data-effect=\"bold\">Step 1. Read<\/strong> the problem.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><strong data-effect=\"bold\">Step 2. Identify<\/strong> what you are looking for.<\/td>\n<td>How many hours (time)<\/td>\n<\/tr>\n<tr>\n<td><strong data-effect=\"bold\">Step 3. Name.<\/strong><br \/>\nChoose a variable to represent it.<\/td>\n<td>Let <em data-effect=\"italics\">t<\/em> = time.<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>d = 798 km<\/p>\n<p>r = 76 km\/h<\/p>\n<p>t = ? hours<\/td>\n<\/tr>\n<tr>\n<td><strong data-effect=\"bold\">Step 4. Translate.<\/strong><br \/>\nWrite the appropriate formula.<\/td>\n<td data-valign=\"bottom\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-785245b9aa407ce266bbbe8ea82703f8_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;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#100;&#61;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"47\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Substitute in the given information.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3d6a31945decf95f1d496d1683797833_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#57;&#56;&#61;&#55;&#54;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"74\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td><strong data-effect=\"bold\">Step 5. Solve<\/strong> the equation.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-5446679216590fde9c5972a3c6dc7617_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;&#49;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#116;&#61;&#49;&#48;&#46;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"61\" style=\"vertical-align: 0px;\" \/> hours<\/td>\n<\/tr>\n<tr>\n<td><strong data-effect=\"bold\">Step 6. Check.<\/strong> Substitute the numbers into<br \/>\nthe formula and make sure the result is a<br \/>\ntrue statement.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-49758ff7eaf36df1266a28a53a66437c_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;&#100;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#114;&#116;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#55;&#57;&#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;&#55;&#54;&#92;&#99;&#100;&#111;&#116;&#32;&#49;&#48;&#46;&#53;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#55;&#57;&#56;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#55;&#57;&#56;&#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=\"134\" style=\"vertical-align: -25px;\" \/><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\"><strong data-effect=\"bold\">Step 7. Answer<\/strong> the question with a complete sentence. Rey\u2019s trip will take 10.5 hours.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168342171016\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168345250678\" data-type=\"exercise\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345450632\" data-type=\"problem\">\n<p>Lee wants to drive from Kamloops to his brother\u2019s apartment in Banff, a distance of 495 km. If he drives at a steady rate of 90 km\/h, how many hours will the trip take?<\/p>\n<\/div>\n<div id=\"fs-id1168345302714\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168345407862\">5 1\/2 hours<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p id=\"fs-id1168345327714\">Yesenia is 168 km from Toronto. If she needs to be in Toronto in 2 hours, at what rate does she need to drive?<\/p>\n<\/div>\n<div id=\"fs-id1168345636492\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168345270054\">84 km\/h<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1 data-type=\"title\">Solve a Formula for a Specific Variable<\/h1>\n<p id=\"fs-id1168345638743\">You are probably familiar with some geometry formulas. A formula is a mathematical description of the relationship between variables. Formulas are also used in the sciences, such as chemistry, physics, and biology. In medicine they are used for calculations for dispensing medicine or determining body mass index. Spreadsheet programs rely on formulas to make calculations. It is important to be familiar with formulas and be able to manipulate them easily.<\/p>\n<p id=\"fs-id1168345376761\">In <a class=\"autogenerated-content\" href=\"#fs-id1168345529730\">(Example 1)<\/a> and <a class=\"autogenerated-content\" href=\"#fs-id1168345454045\">(Example 2)<\/a>, we used the formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b3865773037202207382ec637cb61193_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#100;&#61;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"47\" style=\"vertical-align: 0px;\" \/>. This formula gives the value of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b8bfee3a85664394921a77e26dc3b4bb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#100;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: 0px;\" \/>, distance, when you substitute in the values of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b7d7a2a3cffe496b3845c2475ab426e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;&#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;&#110;&#100;&#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;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"50\" style=\"vertical-align: -1px;\" \/>, the rate and time. But in <a class=\"autogenerated-content\" href=\"#fs-id1168345454045\">(Example 2)<\/a>, we had to find the value of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d9af0c8da890e2a109be7d30ff271872_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\" \/>. We substituted in values of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-33df85cb493fa2a7ba7529be074b98bd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#100;&#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;&#110;&#100;&#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;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"53\" style=\"vertical-align: -1px;\" \/> and then used algebra to solve for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d9af0c8da890e2a109be7d30ff271872_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\" \/>. If you had to do this often, you might wonder why there is not a formula that gives the value of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d9af0c8da890e2a109be7d30ff271872_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\" \/> when you substitute in the values of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-33df85cb493fa2a7ba7529be074b98bd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#100;&#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;&#110;&#100;&#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;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"53\" style=\"vertical-align: -1px;\" \/>. We can make a formula like this by solving the formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b3865773037202207382ec637cb61193_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#100;&#61;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"47\" style=\"vertical-align: 0px;\" \/> for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d9af0c8da890e2a109be7d30ff271872_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<p id=\"fs-id1168345449343\">To solve a formula for a specific variable means to isolate that variable on one side of the equals sign with a coefficient of 1. All other variables and constants are on the other side of the equals sign. To see how to solve a formula for a specific variable, we will start with the distance, rate and time formula.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 3<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345255240\" data-type=\"problem\">\n<p id=\"fs-id1168345455465\">Solve the formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b3865773037202207382ec637cb61193_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#100;&#61;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"47\" style=\"vertical-align: 0px;\" \/> for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d9af0c8da890e2a109be7d30ff271872_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\" \/>:<\/p>\n<ol id=\"fs-id1169751926961\" class=\"circled\" type=\"a\">\n<li>when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b6c6960f0f75a0f6c841782996454ba4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#100;&#61;&#53;&#50;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"60\" style=\"vertical-align: 0px;\" \/> km and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e24c1186ecd2363e56796489786d0f13_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;&#61;&#54;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"49\" style=\"vertical-align: 0px;\" \/> km\/hr<\/li>\n<li>in general<\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id1168345329250\" data-type=\"solution\">\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1168345427139\">We will write the solutions side-by-side to demonstrate that solving a formula in general uses the same steps as when we have numbers to substitute.<\/p>\n<table id=\"fs-id1169149033323\" class=\"unnumbered unstyled\" summary=\"This is a table that has five rows and four columns. The instructions and math within it demonstrate the solving a formula is done the same way for a formula in general and for when actual values are substituted into the formula. The first row, which is a header row, has only two cells: one that spans the first two columns, and one that spans the third and fourth columns. In the header row, the first cell to the left reads: \u201c(a) when d equals 520 and r equals 65.\u201d The second cell reads: \u201c(b) in general.\u201d Below the header row, the first and third columns contain written instructions, and the second and fourth columns show math. In the second row, the first cell reads: \u201cWrite the formula.\u201d The second cell contains the equation d equals r times t. The third cell reads: \u201cWrite the formula.\u201d The fourth cell contains the equation d equals r times t. In the third row, the first cell to the left reads: \u201cSubstitute.\u201d The second cell contains the equation 520 equals 65 times t. The third and fourth cells are left blank. In the fourth row, the first cell to the left reads: \u201cDivide, to isolate t.\u201d The second cell contains the equation 520 over 65 equals 65t over 65. The third cell reads: \u201cDivide, to isolate t.\u201d The fourth cell contains the equation d over r equals the product r times t over r. In the last row, the first cell to the left reads: \u201cSimplify.\u201d The second cell contains the answer to the equation: 8 equals t. The third cell reads: \u201cSimplify.\u201d The fourth cell contains the equation d over r equals t.\" data-label=\"\">\n<tbody>\n<tr>\n<td style=\"width: 401.406px\" colspan=\"2\">a) when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b6c6960f0f75a0f6c841782996454ba4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#100;&#61;&#53;&#50;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"60\" style=\"vertical-align: 0px;\" \/> km and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e24c1186ecd2363e56796489786d0f13_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;&#61;&#54;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"49\" style=\"vertical-align: 0px;\" \/> km\/hr<\/td>\n<td style=\"width: 422.406px\" colspan=\"4\">b) in general<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 147.406px\">Write the formula.<\/td>\n<td style=\"width: 239.406px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-785245b9aa407ce266bbbe8ea82703f8_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;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#100;&#61;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"47\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 225.406px\" colspan=\"3\">Write the formula.<\/td>\n<td style=\"width: 182.406px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b3865773037202207382ec637cb61193_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#100;&#61;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"47\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 147.406px\">Substitute.<\/td>\n<td style=\"width: 239.406px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9cdc4bba0a9b25807aff9b8b591edf78_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#50;&#48;&#61;&#54;&#53;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"74\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 225.406px\" colspan=\"3\"><\/td>\n<td style=\"width: 182.406px\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 147.406px\">Divide, to isolate <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d9af0c8da890e2a109be7d30ff271872_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<td style=\"width: 239.406px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-71ac3b7ba163a64b06173551ccc3430f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#50;&#48;&#125;&#123;&#54;&#53;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#54;&#53;&#116;&#125;&#123;&#54;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"67\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 225.406px\" colspan=\"3\">Divide, to isolate <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d9af0c8da890e2a109be7d30ff271872_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<td style=\"width: 182.406px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b2f10a6988a2194b086cb0c49fec2fd7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#100;&#125;&#123;&#114;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#114;&#116;&#125;&#123;&#114;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"47\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 147.406px\">Simplify.<\/td>\n<td style=\"width: 239.406px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-8dd707fce894a6d3a01834b796535eb9_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;&#49;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#56;&#61;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"39\" style=\"vertical-align: 0px;\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ebed38576f48a6ff5171c4b9247b7495_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#116;&#61;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"39\" style=\"vertical-align: 0px;\" \/> hours<\/td>\n<td style=\"width: 225.406px\" colspan=\"3\">Simplify.<\/td>\n<td style=\"width: 182.406px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-5fd938f2b64f84951d7730ec5785a38f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#100;&#125;&#123;&#114;&#125;&#61;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"39\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1168345511097\">We say the formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-56d6b9213dc41956731d0f2b1c4117e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#116;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#100;&#125;&#123;&#114;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"40\" style=\"vertical-align: -6px;\" \/> is solved for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d9af0c8da890e2a109be7d30ff271872_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168345211803\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168345228073\" data-type=\"exercise\">\n<div id=\"fs-id1168345511495\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345511495\" data-type=\"problem\">\n<p id=\"fs-id1168345303203\">Solve the formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b3865773037202207382ec637cb61193_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#100;&#61;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"47\" style=\"vertical-align: 0px;\" \/> for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-cd833137d9e103974de98771b9013686_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\" \/>:<\/p>\n<p id=\"fs-id1168345545931\">a) when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f62e19c8161db8b38151400a5e414469_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#100;&#61;&#49;&#56;&#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;&#107;&#109;&#32;&#97;&#110;&#100;&#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;&#116;&#61;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"164\" style=\"vertical-align: -1px;\" \/> hr\u00a0 b) in general<\/p>\n<\/div>\n<div id=\"fs-id1168345325302\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168341853951\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-63aa47deeece8141af79bdcc76707155_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;&#61;&#52;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"49\" style=\"vertical-align: 0px;\" \/> km\/hr b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-35c0548dc1be446c722971449129fd78_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#100;&#125;&#123;&#116;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"42\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345287977\" data-type=\"problem\">\n<p id=\"fs-id1168345473398\">Solve the formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b3865773037202207382ec637cb61193_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#100;&#61;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"47\" style=\"vertical-align: 0px;\" \/> for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-cd833137d9e103974de98771b9013686_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\" \/>:<\/p>\n<p id=\"fs-id1168345194497\">a) when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e1af42363e0e72dc55227710c13bc4ad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#100;&#61;&#55;&#56;&#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;&#107;&#109;&#32;&#97;&#110;&#100;&#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;&#116;&#61;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"172\" style=\"vertical-align: -1px;\" \/> hr\u00a0 b) in general<\/p>\n<\/div>\n<div id=\"fs-id1168345217002\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168341959893\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e24c1186ecd2363e56796489786d0f13_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;&#61;&#54;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"49\" style=\"vertical-align: 0px;\" \/> km\/hr\u00a0 b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-35c0548dc1be446c722971449129fd78_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#100;&#125;&#123;&#116;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"42\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168345325302\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 4<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168341863632\" data-type=\"problem\">\n<p id=\"fs-id1168345433028\">Solve the formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-24a2e6b1cf95bdbe7efc1fc627d6b480_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#98;&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"66\" style=\"vertical-align: -6px;\" \/> for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-8251186ed2c7eba82199c8124139e96f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: 0px;\" \/>:<\/p>\n<p>a) when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-496563d63204b34c7c84155fb37c0dbe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;&#61;&#57;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"55\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-90b7f9c1a4b75f42c5c317e6f302e17b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;&#61;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"48\" style=\"vertical-align: 0px;\" \/> b) in general<\/p>\n<\/div>\n<div id=\"fs-id1168345461758\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168463862046\" class=\"unnumbered unstyled\" summary=\"This figure is a table that has six rows and four columns. It shows the written instructions and the math for solving a formula when specific values are given, and for solving the formula in general. The first row, which is a header row, has only two cells: one that spans the first two columns, and one that spans the third and fourth columns. In the header row, the first cell to the left reads: \u201c(a) when A equals 90 and b equals 15.\u201d The second cell reads: \u201c(b) in general.\u201d Below the header row, the first and third columns contain written instructions, and the second and fourth columns show math. In the second row, the first cell reads: \u201cWrite the formula.\u201d The second cell contains the equation A equals \u00bd times b times h. The third cell reads: \u201cWrite the formula.\u201d The fourth cell contains the equation A equals \u00bd times b times h. In the third row, the first cell to the left reads: \u201cSubstitute.\u201d The second cell contains the equation 90 equals \u00bd times 15 times h, with 90 and 15 written in red. The third and fourth cells are left blank. In the fourth row, the first cell to the left reads: \u201cClear the fractions.\u201d The second cell contains the equation 2 times 90 equals 2 times \u00bd times 15 times h, with \u201c2 times\u201d written in red on both sides. The third cell reads: \u201cClear the fractions.\u201d The fourth cell contains the equation 2 times A equals 2 times \u00bd times b times h, with \u201c2 times\u201d written in red on both sides. In the fifth row, the first cell to the left reads: \u201cSimplify.\u201d The second cell contains the equation 180 equals 15 times h. The third cell reads: \u201cSimplify.\u201d The fourth cell contains the equation 2 times A equals b times h. In the last row, the first cell to the left reads: \u201cSolve for h.\u201d The second cell contains the solution to the equation: 12 equals h. The third cell reads: \u201cSolve for h.\u201d The fourth cell contains the solution to the equation: the product 2 times A over b equals h.\" data-label=\"\">\n<tbody>\n<tr>\n<td style=\"width: 295.406px\" colspan=\"2\">a) when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-496563d63204b34c7c84155fb37c0dbe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;&#61;&#57;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"55\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-90b7f9c1a4b75f42c5c317e6f302e17b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;&#61;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"48\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 512.406px\" colspan=\"4\">b) in general<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 128.406px\">Write the formula.<\/td>\n<td style=\"width: 152.406px\"><span id=\"eip-id1168463859550\" data-type=\"media\" data-alt=\".\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-24a2e6b1cf95bdbe7efc1fc627d6b480_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#98;&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"66\" style=\"vertical-align: -6px;\" \/><\/span><\/td>\n<td style=\"width: 335.406px\" colspan=\"3\">Write the formula.<\/td>\n<td style=\"width: 162.406px\"><span id=\"eip-id1168463859564\" data-type=\"media\" data-alt=\".\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-5cb2fb3fbbf604e84b75219ba0d571aa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#32;&#98;&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"66\" style=\"vertical-align: -6px;\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 128.406px\">Substitute.<\/td>\n<td style=\"width: 152.406px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-1e7179814cc4a3494d4ac9d0abd39484_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#48;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#116;&#101;&#120;&#116;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#49;&#53;&#125;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"105\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 335.406px\" colspan=\"3\"><\/td>\n<td style=\"width: 162.406px\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 128.406px\">Clear the fractions.<\/td>\n<td style=\"width: 152.406px\"><span id=\"eip-id1168463859603\" data-type=\"media\" data-alt=\".\"><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-98538c91e5bce419ce72a31160a093b9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#50;&#125;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#57;&#48;&#32;&#61;&#32;&#92;&#116;&#101;&#120;&#116;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#50;&#125;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#32;&#49;&#53;&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"123\" style=\"vertical-align: -6px;\" \/><\/span><\/td>\n<td style=\"width: 335.406px\" colspan=\"3\">Clear the fractions.<\/td>\n<td style=\"width: 162.406px\"><span id=\"eip-id1168463819926\" data-type=\"media\" data-alt=\".\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e4f0009f7e7e8c781c465133d91f6bc1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#50;&#125;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#65;&#32;&#61;&#32;&#92;&#116;&#101;&#120;&#116;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#50;&#125;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#32;&#98;&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"109\" style=\"vertical-align: -6px;\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 128.406px\">Simplify.<\/td>\n<td style=\"width: 152.406px\"><span id=\"eip-id1168463819943\" data-type=\"media\" data-alt=\".\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-27033afcf6b8f261fe48423a4d17b6e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#56;&#48;&#61;&#49;&#53;&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"77\" style=\"vertical-align: 0px;\" \/><\/span><\/td>\n<td style=\"width: 335.406px\" colspan=\"3\">Simplify.<\/td>\n<td style=\"width: 162.406px\"><span id=\"eip-id1168463819957\" data-type=\"media\" data-alt=\".\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-5a32417d24a8e8eab5cd283b737b8456_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#65;&#61;&#98;&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"64\" style=\"vertical-align: 0px;\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 128.406px\">Solve for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-8251186ed2c7eba82199c8124139e96f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<td style=\"width: 152.406px\"><span id=\"eip-id1168463819979\" data-type=\"media\" data-alt=\".\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4a704f6e609c5c23ce55293b79d2e804_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#61;&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"50\" style=\"vertical-align: 0px;\" \/><\/span><\/td>\n<td style=\"width: 335.406px\" colspan=\"3\">Solve for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-8251186ed2c7eba82199c8124139e96f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<td style=\"width: 162.406px\"><span id=\"eip-id1168463819997\" data-type=\"media\" data-alt=\".\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ca71955667bce09ceeeb46795d26f0d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#65;&#125;&#123;&#98;&#125;&#32;&#61;&#32;&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"53\" style=\"vertical-align: -6px;\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1168345723921\">We can now find the height of a triangle, if we know the area and the base, by using the formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b3fb72a1428034227993b2b9518df8f0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#104;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#65;&#125;&#123;&#98;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"54\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168345199361\" class=\"try\" data-type=\"note\">\n<div data-type=\"exercise\">\n<div id=\"fs-id1168345287977\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345389373\" data-type=\"problem\">\n<p id=\"fs-id1168341852742\">Use the formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-24a2e6b1cf95bdbe7efc1fc627d6b480_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#98;&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"66\" style=\"vertical-align: -6px;\" \/> to solve for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-8251186ed2c7eba82199c8124139e96f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: 0px;\" \/>:<\/p>\n<p id=\"fs-id1168345262141\">a) when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d18fb111abaaa4632e756ac7c100da17_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;&#61;&#49;&#55;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"64\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-638156e1dacbcf8c458ae5e112d3b878_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;&#61;&#49;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"49\" style=\"vertical-align: 0px;\" \/> b) in general<\/p>\n<\/div>\n<div id=\"fs-id1168345277861\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168345219463\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-44948fe8ea2a6873d6e5e93a37ffb7a3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#104;&#61;&#50;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"52\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b3fb72a1428034227993b2b9518df8f0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#104;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#65;&#125;&#123;&#98;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"54\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345202847\" data-type=\"problem\">\n<p id=\"fs-id1168345559956\">Use the formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-24a2e6b1cf95bdbe7efc1fc627d6b480_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#98;&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"66\" style=\"vertical-align: -6px;\" \/> to solve for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4e1135b445e2550089a0e7fc0d9a1aca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\" \/>:<\/p>\n<p id=\"fs-id1168345213687\">a) when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e60a1f35b6c6cdfa035498c502cd1544_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;&#61;&#54;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"54\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-07aacc8803368dd547d7e48b67831c03_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#104;&#61;&#51;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"51\" style=\"vertical-align: 0px;\" \/> b) in general<\/p>\n<\/div>\n<div data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168345540818\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9b094a502944d0d9a01558c034d12eaa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;&#61;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"40\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-966ab3127f54d63e227886099dc20181_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#65;&#125;&#123;&#104;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"51\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1168345453615\">The formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-54c80255501568de53985b1688a6fcd9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#73;&#61;&#80;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"61\" style=\"vertical-align: 0px;\" \/> is used to calculate simple interest, <em data-effect=\"italics\">I<\/em>, for a principal, <em data-effect=\"italics\">P<\/em>, invested at rate, <em data-effect=\"italics\">r<\/em>, for <em data-effect=\"italics\">t<\/em> years.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 5<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345291298\" data-type=\"problem\">\n<p id=\"fs-id1168345441444\">Solve the formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-54c80255501568de53985b1688a6fcd9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#73;&#61;&#80;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"61\" style=\"vertical-align: 0px;\" \/> to find the principal, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-5b9d828869ed6c62a532a86ba54cc3d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#80;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\" \/>:<\/p>\n<p class=\"p1\"><span class=\"s1\">a)<\/span> when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e0a2d9d53841c2e93d6f74b7ec148f03_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#73;&#61;&#92;&#36;&#53;&#44;&#54;&#48;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"85\" style=\"vertical-align: -4px;\" \/>, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-40b3e82e3f3a467237d1944c30877e86_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;&#61;&#52;&#92;&#37;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"55\" style=\"vertical-align: -1px;\" \/>, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-0432055615cde1a12d782714b6e78acf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#116;&#61;&#55;&#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;&#121;&#101;&#97;&#114;&#115;&#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;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"86\" style=\"vertical-align: -4px;\" \/> <span class=\"s1\">b)<\/span> in general<\/p>\n<\/div>\n<div data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168463859179\" style=\"width: 100%\" summary=\"This figure is a table that has seven rows and four columns. It shows the written instructions and the math for solving a formula when specific values are given, and for solving the formula in general. The first row, which is a header row, has only two cells: one that spans the first two columns, and one that spans the third and fourth columns. In the header row, the first cell to the left reads: \u201c(a) I equals 5,600 dollars, r equals 4 percent, t equals 7 years.\u201d The second cell reads: \u201c(b) in general.\u201d Below the header row, the first and third columns contain written instructions, and the second and fourth columns show math. In the second row, the first cell reads: \u201cWrite the formula.\u201d The second cell contains the equation I equals P times r times t. The third cell reads: \u201cWrite the formula.\u201d The fourth cell contains the equation I equals P times r times t. In the third row, the first cell to the left reads: \u201cSubstitute.\u201d The second cell contains the equation 5600 equals P times 0.04 times 7. The third and fourth cells are left blank. In the fourth row, the first cell to the left reads: \u201cSimplify.\u201d The second cell contains the equation 5600 equals P times 0.28. The third cell reads: \u201cSimplify.\u201d The fourth cell contains the equation I equals P times the product rt, with r times t written in parentheses. In the fifth row, the first cell to the left reads: \u201cDivide, to isolate P.\u201d The second cell contains the equation 5600 over 0.28 equals the product P times 0.28 over 0.28, with \u201cdivided by 0.28\u201d written in red on both sides. The third cell reads: \u201cDivide, to isolate P.\u201d The fourth cell contains the equation I over the product rt equals the product P times rt, with r times t in parentheses, over the product rt, with divided by the product rt\u201d written in red on both sides. In the sixth row, the first cell to the left reads: \u201cSimplify.\u201d The second cell contains the solution to the equation: 20,000 equals P. The third cell reads: \u201cSimplify.\u201d The fourth cell contains the solution to the equation: I over the product rt equals P. In the last row, the first cell to the left reads: \u201cThe principal is\u201d. The second cell contains the answer 20,000 dollars. The third cell is blank. The fourth cell contains the equation P equals I over the product r t.\" data-label=\"\">\n<tbody>\n<tr style=\"height: 14px\">\n<td style=\"width: 47.5%;height: 14px\" colspan=\"2\">a)<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e0a2d9d53841c2e93d6f74b7ec148f03_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#73;&#61;&#92;&#36;&#53;&#44;&#54;&#48;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"85\" style=\"vertical-align: -4px;\" \/>, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-40b3e82e3f3a467237d1944c30877e86_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;&#61;&#52;&#92;&#37;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"55\" style=\"vertical-align: -1px;\" \/>, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2ff665025f1d1f420c431ae8d80db9c7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#116;&#61;&#55;&#32;&#121;&#101;&#97;&#114;&#115;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"82\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 47.6137%;height: 14px\" colspan=\"2\">b) in general<\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 21.8182%;height: 14px\">Write the formula.<\/td>\n<td style=\"width: 25.6818%;height: 14px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-7f5d373543fe9d33113f9203bf4d34a3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#73;&#32;&#61;&#32;&#80;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"61\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 21.8182%;height: 14px\">Write the formula.<\/td>\n<td style=\"width: 25.7955%;height: 14px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-54c80255501568de53985b1688a6fcd9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#73;&#61;&#80;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"61\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 21.8182%;height: 16px\">Substitute.<\/td>\n<td style=\"width: 25.6818%;height: 16px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f09911397c5932761c1c9f970a14c9d4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#54;&#48;&#48;&#32;&#61;&#32;&#80;&#40;&#48;&#46;&#48;&#52;&#41;&#40;&#55;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"141\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 21.8182%;height: 16px\"><\/td>\n<td style=\"width: 25.7955%;height: 16px\"><\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 21.8182%;height: 16px\">Simplify.<\/td>\n<td style=\"width: 25.6818%;height: 16px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-433a320ed3b610d1d8b85f05b2641810_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#54;&#48;&#48;&#61;&#80;&#40;&#48;&#46;&#50;&#56;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"118\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 21.8182%;height: 16px\">Simplify.<\/td>\n<td style=\"width: 25.7955%;height: 16px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-012a03912b27dd0eb0dc81eda5c604aa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#73;&#32;&#61;&#32;&#80;&#32;&#40;&#114;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"74\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Divide, to isolate <em data-effect=\"italics\">P<\/em>.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-06887812c57e7fd1399aa0167182a15d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#54;&#48;&#48;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#48;&#46;&#50;&#56;&#125;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#80;&#40;&#48;&#46;&#50;&#56;&#41;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#48;&#46;&#50;&#56;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"101\" style=\"vertical-align: -6px;\" \/><\/td>\n<td>Divide, to isolate <em data-effect=\"italics\">P<\/em>.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3fd201561f6dd4bf2e9026ccfa5f7521_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#73;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#114;&#116;&#125;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#80;&#40;&#114;&#116;&#41;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#114;&#116;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"72\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 35px\">\n<td style=\"width: 21.8182%;height: 35px\">Simplify.<\/td>\n<td style=\"width: 25.6818%;height: 35px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b3c641285796edffbd3d4454ed162dec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#48;&#44;&#48;&#48;&#48;&#32;&#61;&#32;&#80;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"90\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 21.8182%;height: 35px\">Simplify.<\/td>\n<td style=\"width: 25.7955%;height: 35px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2796c322d70aa20353eb4a6197418c4a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#73;&#125;&#123;&#114;&#116;&#125;&#61;&#80;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"51\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 36px\">\n<td style=\"width: 21.8182%;height: 36px\">The principal is<\/td>\n<td style=\"width: 25.6818%;height: 36px\">$<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-84b3cc6d808881d6d2630cf23ef46761_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#48;&#44;&#48;&#48;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"53\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 21.8182%;height: 36px\"><\/td>\n<td style=\"width: 25.7955%;height: 36px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-6f3bffecf4cd82fdc928768b3d708dd3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#80;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#73;&#125;&#123;&#114;&#116;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"51\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168342181314\" data-type=\"problem\">\n<p id=\"fs-id1168345638820\">Use the formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-54c80255501568de53985b1688a6fcd9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#73;&#61;&#80;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"61\" style=\"vertical-align: 0px;\" \/> to find the principal, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-5b9d828869ed6c62a532a86ba54cc3d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#80;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\" \/>:<\/p>\n<p id=\"fs-id1168341889957\">a) when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-864b0a6759618e716eb8faba8a59976a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#73;&#61;&#92;&#36;&#50;&#44;&#49;&#54;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"85\" style=\"vertical-align: -4px;\" \/>, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-1a1a8cd5bff6ada513b711c68f8d436f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;&#61;&#54;&#92;&#37;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"55\" style=\"vertical-align: -1px;\" \/>, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-64d84df8776491c0f9b0933b73605c39_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#116;&#61;&#51;&#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;&#121;&#101;&#97;&#114;&#115;&#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;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"86\" style=\"vertical-align: -4px;\" \/> b) in general<\/p>\n<\/div>\n<div id=\"fs-id1168345669118\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168345745251\">a) &#36;12,000 b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-6f3bffecf4cd82fdc928768b3d708dd3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#80;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#73;&#125;&#123;&#114;&#116;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"51\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p id=\"fs-id1168345445798\">Use the formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-54c80255501568de53985b1688a6fcd9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#73;&#61;&#80;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"61\" style=\"vertical-align: 0px;\" \/> to find the principal,<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-5b9d828869ed6c62a532a86ba54cc3d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#80;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\" \/>:<\/p>\n<p id=\"fs-id1168345678089\">a) when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-c21b2b873011f4efe6bcbe8639f42e7e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#73;&#61;&#92;&#36;&#53;&#44;&#52;&#48;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"85\" style=\"vertical-align: -4px;\" \/>, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-c2c71cab5168b2daf567d87d04f4857c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;&#61;&#49;&#50;&#92;&#37;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"64\" style=\"vertical-align: -1px;\" \/>, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e3b5eafa2e163d73b2cb8601935f1e80_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#116;&#61;&#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;&#121;&#101;&#97;&#114;&#115;&#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;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"86\" style=\"vertical-align: -4px;\" \/> b) in general<\/p>\n<\/div>\n<div id=\"fs-id1168341906686\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168345398353\">a) $9,000 b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-6f3bffecf4cd82fdc928768b3d708dd3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#80;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#73;&#125;&#123;&#114;&#116;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"51\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1168345486708\">Later in this class, and in future algebra classes, you\u2019ll encounter equations that relate two variables, usually <em data-effect=\"italics\">x<\/em> and <em data-effect=\"italics\">y<\/em>. You might be given an equation that is solved for <em data-effect=\"italics\">y<\/em> and need to solve it for <em data-effect=\"italics\">x<\/em>, or vice versa. In the following example, we\u2019re given an equation with both <em data-effect=\"italics\">x<\/em> and <em data-effect=\"italics\">y<\/em> on the same side and we\u2019ll solve it for <em data-effect=\"italics\">y<\/em>.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 6<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345229876\" data-type=\"problem\">\n<p id=\"fs-id1168345229878\">Solve the formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4fc942c69b32321f3d63bd60b2fe5704_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;&#43;&#50;&#121;&#61;&#49;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"100\" style=\"vertical-align: -4px;\" \/> for <em data-effect=\"italics\">y<\/em>:<\/p>\n<p id=\"fs-id1168345427096\">a) when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f7c85ff287e1ef81cbd9649e2566aada_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\" \/> b) in general<\/p>\n<\/div>\n<div id=\"fs-id1168341917214\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168463888057\" style=\"width: 100%\" summary=\"This figure is a table that has seven rows and four columns. It shows the written instructions and the math for solving a formula when specific values are given, and for solving the formula in general. The first row, which is a header row, has only two cells: one that spans the first two columns, and one that spans the third and fourth columns. In the header row, the first cell to the left reads: \u201c(a) when x equals 4\u201d The second cell reads: \u201c(b) in general.\u201d Below the header row, the first and third columns contain written instructions, and the second and fourth columns show math. In the second row, the first cell is left blank. The second cell contains the equation 3 x plus 2 y equals 18. The third cell is left blank. The fourth cell contains the equation 3 x plus 2 y equals 18. In the third row, the first cell to the left reads: \u201cSubstitute.\u201d The second cell contains the equation 3 times 4 plus 2 y equals 18. The third and fourth cells are left blank. In the fourth row, the first cell to the left reads: \u201cSubtract to isolate the y-term.\u201d The second cell contains the equation 12 minus 12 plus 2 y equals 18 minus 12, with \u201cminus 12\u201d written in red on both sides. The third cell reads: \u201cSubtract to isolate the y-term.\u201d The fourth cell contains the equation 3 x minus 3 x plus 2 y equals 18 minus 3 x, with \u201cminus 3x\u201d written in red on both sides. In the fifth row, the first cell to the left reads: \u201cDivide.\u201d The second cell contains the equation the product 2 y over 2 equals 6 over 2, with \u201cdivided by 2\u201d written in red on both sides. The third cell reads: \u201cDivide.\u201d The fourth cell contains the equation the product 2 y over 2 equals 18 over 2 minus the product 3x over 2, with \u201cdivide by 2\u201d written in red for each term. In the last row, the first cell to the left reads: \u201cSimplify.\u201d The second cell contains the solution to the equation: y equals 3. The third cell reads: \u201cSimplify.\u201d The fourth cell contains the solution to the equation: y equals negative product 3 x over 2 plus 9.\" data-label=\"\">\n<tbody>\n<tr>\n<td style=\"width: 50.2273%\" colspan=\"2\">a) when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f7c85ff287e1ef81cbd9649e2566aada_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 49.6591%\" colspan=\"2\">b) in general<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 21.25%\"><\/td>\n<td style=\"width: 28.9773%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4fc942c69b32321f3d63bd60b2fe5704_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;&#43;&#50;&#121;&#61;&#49;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"100\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 21.25%\"><\/td>\n<td style=\"width: 28.4091%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4fc942c69b32321f3d63bd60b2fe5704_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;&#43;&#50;&#121;&#61;&#49;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"100\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 21.25%\">Substitute.<\/td>\n<td style=\"width: 28.9773%\"><span id=\"eip-id1168463876160\" data-type=\"media\" data-alt=\".\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-bd0516b9943d72ef7d3142740613d904_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#40;&#92;&#116;&#101;&#120;&#116;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#52;&#125;&#41;&#43;&#50;&#121;&#61;&#49;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"113\" style=\"vertical-align: -5px;\" \/><\/span><\/td>\n<td style=\"width: 21.25%\"><\/td>\n<td style=\"width: 28.4091%\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 21.25%\">Subtract to isolate the<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-15f1a95c39a36eda2e95d509a5f0f8b9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/>-term.<\/td>\n<td style=\"width: 28.9773%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-5d9544f287c7ce7d69aa3f10ce21f89e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#103;&#97;&#116;&#104;&#101;&#114;&#101;&#100;&#125;&#32;&#49;&#50;&#92;&#116;&#101;&#120;&#116;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#45;&#49;&#50;&#125;&#43;&#50;&#121;&#61;&#49;&#56;&#92;&#116;&#101;&#120;&#116;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#45;&#49;&#50;&#125;&#92;&#92;&#32;&#50;&#121;&#61;&#54;&#92;&#92;&#32;&#92;&#101;&#110;&#100;&#123;&#103;&#97;&#116;&#104;&#101;&#114;&#101;&#100;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"161\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 21.25%\">Subtract to isolate the<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-15f1a95c39a36eda2e95d509a5f0f8b9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/>-term.<\/td>\n<td style=\"width: 28.4091%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-aaef3b5b09616c103df208a6c5bbdfb3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#103;&#97;&#116;&#104;&#101;&#114;&#101;&#100;&#125;&#32;&#51;&#120;&#92;&#116;&#101;&#120;&#116;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#45;&#51;&#120;&#125;&#43;&#50;&#121;&#61;&#49;&#56;&#92;&#116;&#101;&#120;&#116;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#45;&#51;&#120;&#125;&#92;&#92;&#32;&#50;&#121;&#61;&#49;&#56;&#45;&#51;&#120;&#92;&#92;&#32;&#92;&#101;&#110;&#100;&#123;&#103;&#97;&#116;&#104;&#101;&#114;&#101;&#100;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"166\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 21.25%\">Divide.<\/td>\n<td style=\"width: 28.9773%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b179f5bf743a90e3abb61b2ee54ae5d0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#121;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#50;&#125;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#54;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"49\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 21.25%\">Divide.<\/td>\n<td style=\"width: 28.4091%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-c202e5bc5635f8b314848f561cabeb84_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#121;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#50;&#125;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#56;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#50;&#125;&#125;&#45;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#120;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"96\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 21.25%\">Simplify.<\/td>\n<td style=\"width: 28.9773%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b1c47a5f94466d178d330835fd0eba66_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"42\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 21.25%\">Simplify.<\/td>\n<td style=\"width: 28.4091%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-0083cbf69c292cbdc44c2bd39725c693_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#57;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#50;&#125;&#32;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"84\" style=\"vertical-align: -6px;\" \/><br \/>\nor<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f7cf724a402a6415124170f9603372b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#50;&#125;&#32;&#120;&#43;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"98\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168341973908\" data-type=\"problem\">\n<p id=\"fs-id1168345445835\">Solve the formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-80cb78b3684c3ba468977607c1266342_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;&#43;&#52;&#121;&#61;&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"100\" style=\"vertical-align: -4px;\" \/> for <em data-effect=\"italics\">y<\/em>:<\/p>\n<p id=\"fs-id1168345572426\">a) when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-41b6eadfa5fac30210c92d49aed10661_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#52;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"50\" style=\"vertical-align: -6px;\" \/> \u00a0\u00a0\u00a0 b) in general<\/p>\n<\/div>\n<div id=\"fs-id1168341960142\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168345423533\">a)<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-6e65c51830a54e94d76eccd2df07f375_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"55\" style=\"vertical-align: -4px;\" \/> \u00a0\u00a0\u00a0 b)<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-cb3699228ab70d03b2950cca6f93ff42_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#48;&#45;&#51;&#120;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"75\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TY IT 6.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345558322\" data-type=\"problem\">\n<p id=\"fs-id1168345558324\">Solve the formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-1da3d26266c0a63030b4ad1017b4834c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#120;&#43;&#50;&#121;&#61;&#49;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"100\" style=\"vertical-align: -4px;\" \/> for <em data-effect=\"italics\">y:<\/em><\/p>\n<p id=\"fs-id1168342046117\">a) when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f7c85ff287e1ef81cbd9649e2566aada_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\" \/> \u00a0\u00a0\u00a0 b) in general<\/p>\n<\/div>\n<div id=\"fs-id1168342180725\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168342180727\">a)<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-6e65c51830a54e94d76eccd2df07f375_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"55\" style=\"vertical-align: -4px;\" \/>\u00a0 \u00a0\u00a0\u00a0\u00a0 b)<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-68ca681275fe21e2e9fd3a482afd07d4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#56;&#45;&#53;&#120;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"75\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169751859527\">Now we will solve a formula in general without using numbers as a guide.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 7<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345385685\" data-type=\"problem\">\n<p id=\"fs-id1168345423448\">Solve the formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-52bc09baef452b95c6c682681a76aa7e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#80;&#61;&#97;&#43;&#98;&#43;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"106\" style=\"vertical-align: -2px;\" \/> for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3e9c4cc6ee8914c6fb4d5253abf7fc46_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1168345456529\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168463887699\" style=\"width: 100%\" summary=\"This figure is has two columns, with written instructions on the left and math on the right. At the top of the figure on the left, the instructions say: \u201cWe will isolate a on one side of the equation.\u201d To the right of this instruction is the original equation: P equals a plus b plus c. One line down on the left, the instructions say: \u201cBoth b and c are added to a, so we subtract them from both sides of the equation.\u201d To the right of this sentence is the original equation with b and c subtracted from both sides of the equation: P minus b minus c equals a plus b plus c minus b minus c, with \u201cminus b minus c\u201d written in red on both sides. Another line down on the left, the instructions say: \u201cSimplify.\u201d To the right of this instruction is the equation P minus b minus c equals a. Below this is the equation a equals P minus b minus c.\" data-label=\"\">\n<tbody>\n<tr>\n<td>We will isolate <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3e9c4cc6ee8914c6fb4d5253abf7fc46_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> on one side of the equation.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-52bc09baef452b95c6c682681a76aa7e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#80;&#61;&#97;&#43;&#98;&#43;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"106\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Both <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4e1135b445e2550089a0e7fc0d9a1aca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-77479b59a494b611004da289deb0dfa3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\" \/> are added to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3e9c4cc6ee8914c6fb4d5253abf7fc46_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/>, so we subtract them from both sides of the equation.<\/td>\n<td><span id=\"eip-id1168463887754\" data-type=\"media\" data-alt=\".\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-11aa45c5210d52261fe595a012cb8bf3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#80;&#32;&#92;&#116;&#101;&#120;&#116;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#45;&#98;&#45;&#99;&#125;&#32;&#61;&#32;&#97;&#43;&#98;&#43;&#99;&#32;&#92;&#116;&#101;&#120;&#116;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#45;&#98;&#45;&#99;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"207\" style=\"vertical-align: -2px;\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b893cccbd851c1e7740ce35b6005fc36_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#103;&#97;&#116;&#104;&#101;&#114;&#101;&#100;&#125;&#32;&#80;&#45;&#98;&#45;&#99;&#61;&#97;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#111;&#114;&#125;&#32;&#92;&#92;&#32;&#97;&#61;&#80;&#45;&#98;&#45;&#99;&#32;&#92;&#101;&#110;&#100;&#123;&#103;&#97;&#116;&#104;&#101;&#114;&#101;&#100;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"106\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168345539191\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168345539194\" data-type=\"exercise\">\n<div id=\"fs-id1168345539196\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Solve the formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-52bc09baef452b95c6c682681a76aa7e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#80;&#61;&#97;&#43;&#98;&#43;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"106\" style=\"vertical-align: -2px;\" \/> for <em>b<\/em>.<\/p>\n<div id=\"fs-id1168345622774\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168345622777\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ae872c5fdbab4e6626951069ea7e8c9f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;&#61;&#80;&#45;&#97;&#45;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"106\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345543450\" data-type=\"problem\">\n<p id=\"fs-id1168345543452\">Solve the formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-52bc09baef452b95c6c682681a76aa7e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#80;&#61;&#97;&#43;&#98;&#43;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"106\" style=\"vertical-align: -2px;\" \/> for <em data-effect=\"italics\">c<\/em>.<\/p>\n<\/div>\n<div id=\"fs-id1168341906957\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168341906959\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-664928cc7eac7b5b1fc760859c9e70b9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;&#61;&#80;&#45;&#97;&#45;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"106\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168345543445\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168345543448\" data-type=\"exercise\">\n<div id=\"fs-id1168341906957\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 8<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345621361\" data-type=\"problem\">\n<p id=\"fs-id1168345621363\">Solve the formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-076678d124eb8a23e741ce843319958f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#120;&#43;&#53;&#121;&#61;&#49;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"100\" style=\"vertical-align: -4px;\" \/> for <em data-effect=\"italics\">y.<\/em><\/p>\n<\/div>\n<div id=\"fs-id1168345525269\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168462677762\" style=\"width: 100%\" summary=\"This figure has two columns, with written instructions on the left and math on the right. At the top of the figure on the right is the equation 6x plus 5 y equals 13. One line down on the left, the instructions say: \u201cSubtract 6 x from both sides to isolate the term with y. To the right of this sentence is the original equation with 6x subtracted from both sides: 6 x minus 6 x plus 5y equals 13 minus 6x, with \u201cminus 6 x\u201d written in red on both sides. Another line down on the left, the instructions say: \u201cSimplify.\u201d To the right of this word is the equation 5y equals 13 minus 6 x. One more line down on the left, the instructions say: \u201cDivide by 5 to make the coefficient 1.\u201d To the right of this instruction is the equation with both sides divided by 5: 5y over 5 equals the difference 13 minus 6 x over 5, with \u201cdivided by 5\u201d written in red on both sides. One more line down on the left, the instructions say: \u201cSimplify.\u201d To the right of this word is the equation y equals the difference 13 minus 6 x over 5.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-076678d124eb8a23e741ce843319958f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#120;&#43;&#53;&#121;&#61;&#49;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"100\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Subtract <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e9f519402419cb8391826b05768074c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"19\" style=\"vertical-align: 0px;\" \/> from both sides to isolate the term with <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-15f1a95c39a36eda2e95d509a5f0f8b9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/>.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-454039981a5d318072fc8013fe2f50b4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#120;&#32;&#92;&#116;&#101;&#120;&#116;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#45;&#54;&#120;&#125;&#32;&#43;&#53;&#121;&#32;&#61;&#32;&#49;&#51;&#32;&#92;&#116;&#101;&#120;&#116;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#45;&#54;&#120;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"166\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-68dc424faf6407167a6d61d027e324c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#121;&#61;&#49;&#51;&#45;&#54;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"100\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Divide by 5 to make the coefficient 1.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-02a8d28f323187d28499654894fbc93c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#121;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#53;&#125;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#51;&#45;&#54;&#120;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"82\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d1024f81bc75aef7572ff6558f970890_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#51;&#45;&#54;&#120;&#125;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"75\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1168342104215\">The fraction is simplified. We cannot divide <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-af2321ecc6de65ca6b9ea6c793c6867a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#51;&#45;&#54;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"57\" style=\"vertical-align: 0px;\" \/> by 5<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1168342168215\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1168342168219\" data-type=\"exercise\">\n<div id=\"fs-id1168342168221\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168342168221\" data-type=\"problem\">\n<p id=\"fs-id1168342168223\">Solve the formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9cc8f65a8f4f6e8294e80ca08a93c490_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#120;&#43;&#55;&#121;&#61;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"91\" style=\"vertical-align: -4px;\" \/> for <em data-effect=\"italics\">y.<\/em><\/p>\n<\/div>\n<div id=\"fs-id1168345621178\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168345621180\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-6b185a27e58b61e86d1cda76d7312567_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#57;&#45;&#52;&#120;&#125;&#123;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"68\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1168345542275\" data-type=\"problem\">\n<p id=\"fs-id1168345542278\">Solve the formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-fa553c8afdb09c87ea8cc26388dc0ee3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#120;&#43;&#56;&#121;&#61;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"90\" style=\"vertical-align: -4px;\" \/> for <em data-effect=\"italics\">y.<\/em><\/p>\n<\/div>\n<div id=\"fs-id1168345424572\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1168345424574\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-53ae7e32f15e8710dc56da6c048bb4d0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#45;&#53;&#120;&#125;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"68\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1 data-type=\"title\">Key Concepts<\/h1>\n<ul id=\"fs-id1168345670000\" data-bullet-style=\"bullet\">\n<li><strong data-effect=\"bold\">To Solve an Application (with a formula)<\/strong>\n<ol id=\"fs-id1168345670010\" class=\"stepwise\" type=\"1\">\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 we are looking for.<\/li>\n<li><strong data-effect=\"bold\">Name<\/strong> what we are looking for. Choose a variable to represent that quantity.<\/li>\n<li><strong data-effect=\"bold\">Translate<\/strong> into an equation. Write the appropriate formula for the situation. Substitute in the given information.<\/li>\n<li><strong data-effect=\"bold\">Solve<\/strong> the equation using good algebra techniques.<\/li>\n<li><strong data-effect=\"bold\">Check<\/strong> the answer in the problem and 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\">Distance, Rate and Time<\/strong><br \/>\nFor an object moving at a uniform (constant) rate, the distance traveled, the elapsed time, and the rate are related by the formula: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b3865773037202207382ec637cb61193_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#100;&#61;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"47\" style=\"vertical-align: 0px;\" \/> where <em data-effect=\"italics\">d<\/em> = distance, <em data-effect=\"italics\">r<\/em> = rate, <em data-effect=\"italics\">t<\/em> = time.<\/li>\n<li><strong data-effect=\"bold\">To solve a formula for a specific variable<\/strong> means to get that variable by itself with a coefficient of 1 on one side of the equation and all other variables and constants on the other side.<\/li>\n<\/ul>\n<h1 data-type=\"title\">Practice Makes Perfect<\/h1>\n<h2 id=\"fs-id1168345726412\">Use the Distance, Rate, and Time Formula<\/h2>\n<p id=\"fs-id1169754187572\">In the following exercises, solve.<\/p>\n<table style=\"border-collapse: collapse;width: 100%;height: 352px\">\n<tbody>\n<tr>\n<td style=\"width: 51.3711%\">1. Socorro drove for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-8421ec4aa33d9f2fdaabf6433648e9a4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"18\" style=\"vertical-align: -6px;\" \/> hours at 60 miles per hour. How much distance did she travel?<\/td>\n<td style=\"width: 48.6289%\">2. Steve drove for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-c06cc0905d27bb9966c5fe0067446116_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"18\" style=\"vertical-align: -6px;\" \/> hours at 72 miles per hour. How much distance did he travel?<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 51.3711%\">3. Francie rode her bike for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ddc3a8677ede26ad6f05799491b28f0c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"18\" style=\"vertical-align: -6px;\" \/> hours at 12 miles per hour. How far did she ride?<\/td>\n<td style=\"width: 48.6289%\">4. Yuki walked for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-8e6d0df5c41a1b9eeaa84051b9ba6450_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"17\" style=\"vertical-align: -6px;\" \/> hours at 4 miles per hour. How far did she walk?<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 51.3711%\">5. Marta is taking the bus from Abbotsford to Cranbrook. The distance is 774 km and the bus travels at a steady rate of 86 miles per hour. How long will the bus ride be?<\/td>\n<td style=\"width: 48.6289%\">6. Connor wants to drive from Vancouver to the Nakusp, a distance of 630 km. If he drives at a steady rate of 90 km\/h, how many hours will the trip take?<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 51.3711%\">7. Kareem wants to ride his bike from Golden, BC to Banff, AB. The distance is 140 km. If he rides at a steady rate of 20 km\/h, how many hours will the trip take?<\/td>\n<td style=\"width: 48.6289%\">8. Aurelia is driving from Calgary to Edmonton at a rate of 85 km\/h. The distance is 300 km. To the nearest tenth of an hour, how long will the trip take?<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 51.3711%\">9. Alejandra is driving to Prince George, 450 km away. If she wants to be there in 6 hours, at what rate does she need to drive?<\/td>\n<td style=\"width: 48.6289%\">10. Javier is driving to Vernon, 240 km away. If he needs to be in Vernon in 3 hours, at what rate does he need to drive?<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 51.3711%\">11. Philip got a ride with a friend from Calgary to Kelowna, a distance of 890 km. If the trip took 10 hours, how fast was the friend driving?<\/td>\n<td style=\"width: 48.6289%\">12. Aisha took the train from Spokane to Seattle. The distance is 280 miles and the trip took 3.5 hours. What was the speed of the train?<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1168345688676\">Solve a Formula for a Specific Variable<\/h2>\n<table>\n<tbody>\n<tr>\n<td>13. Solve for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d9af0c8da890e2a109be7d30ff271872_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\" \/> using <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b3865773037202207382ec637cb61193_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#100;&#61;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"47\" style=\"vertical-align: 0px;\" \/><\/p>\n<ol style=\"list-style-type: lower-alpha\">\n<li>when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-14ead01e419f83cbc8528177cc8afe10_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#100;&#61;&#50;&#52;&#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;&#110;&#100;&#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;&#61;&#54;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"145\" style=\"vertical-align: -1px;\" \/><\/li>\n<li>in general<\/li>\n<\/ol>\n<\/td>\n<td>14. Solve for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d9af0c8da890e2a109be7d30ff271872_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\" \/> using <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b3865773037202207382ec637cb61193_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#100;&#61;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"47\" style=\"vertical-align: 0px;\" \/><\/p>\n<ol style=\"list-style-type: lower-alpha\">\n<li>when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2051b0092e5135b3dfdd120d2213f5ae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#100;&#61;&#51;&#53;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"60\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-cbfd2a3c7faff56d4512139a2756b2d2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;&#61;&#55;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"50\" style=\"vertical-align: 0px;\" \/><\/li>\n<li>in general<\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<tr>\n<td>15. Solve for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d9af0c8da890e2a109be7d30ff271872_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\" \/> using <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b3865773037202207382ec637cb61193_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#100;&#61;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"47\" style=\"vertical-align: 0px;\" \/><\/p>\n<ol style=\"list-style-type: lower-alpha\">\n<li>when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-1b48b882d1d2ae4db5bc9661ad685753_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#100;&#61;&#49;&#55;&#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;&#97;&#110;&#100;&#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;&#61;&#53;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"145\" style=\"vertical-align: -1px;\" \/><\/li>\n<li>in general<\/li>\n<\/ol>\n<\/td>\n<td>16. Solve for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d9af0c8da890e2a109be7d30ff271872_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\" \/> using <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b3865773037202207382ec637cb61193_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#100;&#61;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"47\" style=\"vertical-align: 0px;\" \/><\/p>\n<ol style=\"list-style-type: lower-alpha\">\n<li>when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-5f3127623d9cd33f8262e6bd1a3b5688_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#100;&#61;&#53;&#49;&#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;&#110;&#100;&#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;&#61;&#54;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"145\" style=\"vertical-align: -1px;\" \/><\/li>\n<li>in general<\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<tr>\n<td>17. Solve for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-cd833137d9e103974de98771b9013686_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\" \/> using <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b3865773037202207382ec637cb61193_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#100;&#61;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"47\" style=\"vertical-align: 0px;\" \/><\/p>\n<ol style=\"list-style-type: lower-alpha\">\n<li>when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d7cb65dea79d8fa988fb07280e1cc8a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#100;&#61;&#52;&#50;&#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;&#110;&#100;&#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;&#116;&#61;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"134\" style=\"vertical-align: -1px;\" \/><\/li>\n<li>in general<\/li>\n<\/ol>\n<\/td>\n<td>18. Solve for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-cd833137d9e103974de98771b9013686_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\" \/> using\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b3865773037202207382ec637cb61193_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#100;&#61;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"47\" style=\"vertical-align: 0px;\" \/><\/p>\n<ol style=\"list-style-type: lower-alpha\">\n<li>when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-8307bfbd64c7e0387d79552cb66d5238_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#100;&#61;&#50;&#48;&#52;&#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;&#110;&#100;&#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;&#116;&#61;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"134\" style=\"vertical-align: -1px;\" \/><\/li>\n<li>in general<\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<tr>\n<td>\n<div data-type=\"exercise\">\n<div data-type=\"problem\">\n<p>19. Solve for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-cd833137d9e103974de98771b9013686_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\" \/> using\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b3865773037202207382ec637cb61193_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#100;&#61;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"47\" style=\"vertical-align: 0px;\" \/><\/p>\n<ol style=\"list-style-type: lower-alpha\">\n<li>when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-45963264ec743117068f37a281cbbc29_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#100;&#61;&#49;&#56;&#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;&#110;&#100;&#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;&#116;&#61;&#52;&#46;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"147\" style=\"vertical-align: -1px;\" \/><\/li>\n<li>in general<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/td>\n<td>20. Solve for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-cd833137d9e103974de98771b9013686_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\" \/> using\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b3865773037202207382ec637cb61193_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#100;&#61;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"47\" style=\"vertical-align: 0px;\" \/><\/p>\n<ol style=\"list-style-type: lower-alpha\">\n<li>when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4796c891a813001d0bc62ef02988ce6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#100;&#61;&#49;&#54;&#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;&#110;&#100;&#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;&#116;&#61;&#50;&#46;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"147\" style=\"vertical-align: -1px;\" \/><\/li>\n<li>in general<\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<tr>\n<td>21. Solve for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-8251186ed2c7eba82199c8124139e96f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: 0px;\" \/> using <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-24a2e6b1cf95bdbe7efc1fc627d6b480_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#98;&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"66\" style=\"vertical-align: -6px;\" \/><\/p>\n<ol style=\"list-style-type: lower-alpha\">\n<li>when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-cfb7cd2a9d1da24f203f0a308660f280_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;&#61;&#49;&#55;&#54;&#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;&#110;&#100;&#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;&#98;&#61;&#50;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"147\" style=\"vertical-align: -1px;\" \/><\/li>\n<li>in general<\/li>\n<\/ol>\n<\/td>\n<td>22. Solve for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4e1135b445e2550089a0e7fc0d9a1aca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\" \/> using <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-24a2e6b1cf95bdbe7efc1fc627d6b480_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#98;&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"66\" style=\"vertical-align: -6px;\" \/><\/p>\n<ol style=\"list-style-type: lower-alpha\">\n<li>when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-1f2dc5c903ce472d6982ed84056f090a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;&#61;&#49;&#50;&#54;&#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;&#110;&#100;&#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;&#49;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"151\" style=\"vertical-align: -1px;\" \/><\/li>\n<li>in general<\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<tr>\n<td>23. Solve for the principal, P using <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-7f5d373543fe9d33113f9203bf4d34a3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#73;&#32;&#61;&#32;&#80;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"61\" style=\"vertical-align: 0px;\" \/>\u00a0 for<\/p>\n<ol style=\"list-style-type: lower-alpha\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-40b2e94c440d5eee1e775e7911afe897_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#73;&#61;&#92;&#36;&#53;&#44;&#52;&#56;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"85\" style=\"vertical-align: -4px;\" \/>,<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-40b3e82e3f3a467237d1944c30877e86_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;&#61;&#52;&#92;&#37;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"55\" style=\"vertical-align: -1px;\" \/>,<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9a6168e1b5dc5cc9169bb9c40709705f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#116;&#61;&#55;&#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;&#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;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"82\" style=\"vertical-align: -4px;\" \/><\/li>\n<li>in general<\/li>\n<\/ol>\n<\/td>\n<td>\n<div data-type=\"exercise\">\n<div data-type=\"problem\">24. Solve for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4e1135b445e2550089a0e7fc0d9a1aca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\" \/> using <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-24a2e6b1cf95bdbe7efc1fc627d6b480_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#98;&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"66\" style=\"vertical-align: -6px;\" \/><\/div>\n<ol style=\"list-style-type: lower-alpha\">\n<li data-type=\"problem\">when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4a4fed36b552f80a6787a2c1f16dbd23_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;&#61;&#54;&#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;&#97;&#110;&#100;&#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;&#49;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"142\" style=\"vertical-align: -1px;\" \/><\/li>\n<li data-type=\"problem\">in general.<\/li>\n<\/ol>\n<\/div>\n<\/td>\n<\/tr>\n<tr>\n<td>25. Solve for the time, t\u00a0 using <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-7f5d373543fe9d33113f9203bf4d34a3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#73;&#32;&#61;&#32;&#80;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"61\" style=\"vertical-align: 0px;\" \/> for<\/p>\n<ol style=\"list-style-type: lower-alpha\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-7c37143882587dbe4950bd50cf29a9a1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#73;&#61;&#92;&#36;&#50;&#44;&#51;&#55;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"85\" style=\"vertical-align: -4px;\" \/>,<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-7e278cf88f526446183a30162ad981b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#80;&#61;&#92;&#36;&#57;&#44;&#48;&#48;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"90\" style=\"vertical-align: -4px;\" \/> ,<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-59432ea5f33c0805411a616af5b3ab04_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;&#61;&#52;&#46;&#52;&#92;&#37;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"69\" style=\"vertical-align: -1px;\" \/><\/li>\n<li>in general<\/li>\n<\/ol>\n<\/td>\n<td>26. Solve for the principal, P using <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-7f5d373543fe9d33113f9203bf4d34a3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#73;&#32;&#61;&#32;&#80;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"61\" style=\"vertical-align: 0px;\" \/> for<\/p>\n<ol style=\"list-style-type: lower-alpha\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9eb0585dc074ed1567241e78bc71b30d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#73;&#61;&#92;&#36;&#51;&#44;&#57;&#53;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"85\" style=\"vertical-align: -4px;\" \/>,<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-1a1a8cd5bff6ada513b711c68f8d436f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;&#61;&#54;&#92;&#37;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"55\" style=\"vertical-align: -1px;\" \/>,<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ddc8d8e9ffab6ac8baaf5969e2c6bdba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#116;&#61;&#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;&#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;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"82\" style=\"vertical-align: -4px;\" \/><\/li>\n<li>in general<\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<tr>\n<td>27. Solve the formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ebeb3988639c2c4bed48af56e200b55d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#43;&#51;&#121;&#61;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"99\" style=\"vertical-align: -4px;\" \/> for y when<\/p>\n<ol style=\"list-style-type: lower-alpha\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-8f4c396d6fb5a0cd1f84a9b5871e52e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\" \/><\/li>\n<li>in general<\/li>\n<\/ol>\n<\/td>\n<td>\n<div data-type=\"exercise\">\n<div data-type=\"problem\">28. Solve for the time, t for<\/div>\n<ol style=\"list-style-type: lower-alpha\">\n<li data-type=\"problem\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-33095c8c298e9282d4d1bf1989b4f82f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#73;&#61;&#92;&#36;&#54;&#50;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"69\" style=\"vertical-align: -1px;\" \/>,<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-70d64af414ca2e1061e6c78149ba429e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#80;&#61;&#92;&#36;&#54;&#44;&#48;&#48;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"90\" style=\"vertical-align: -4px;\" \/>,<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-c596e8362efa22a444115a0d270eb2af_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;&#61;&#53;&#46;&#50;&#92;&#37;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"69\" style=\"vertical-align: -1px;\" \/><\/li>\n<li data-type=\"problem\">in general<\/li>\n<\/ol>\n<\/div>\n<\/td>\n<\/tr>\n<tr>\n<td>29. Solve the formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-614f3a255ab574d667b1754451b84290_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;&#45;&#121;&#61;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"83\" style=\"vertical-align: -4px;\" \/> for y when<\/p>\n<ol style=\"list-style-type: lower-alpha\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-6b8ffae105ca6d71b769a15b83e5cd66_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"56\" style=\"vertical-align: 0px;\" \/><\/li>\n<li>in general<\/li>\n<\/ol>\n<\/td>\n<td>30. Solve the formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-680b4d920b0f8ad388942406e715cb17_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#120;&#43;&#50;&#121;&#61;&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"100\" style=\"vertical-align: -4px;\" \/> for y when<\/p>\n<ol style=\"list-style-type: lower-alpha\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f7c85ff287e1ef81cbd9649e2566aada_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\" \/><\/li>\n<li>in general<\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<tr>\n<td>31. Solve <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e985e0efdbb2b282446fccd3a40795a1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#43;&#98;&#61;&#57;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"80\" style=\"vertical-align: -2px;\" \/> for<\/p>\n<ol style=\"list-style-type: lower-alpha\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3e9c4cc6ee8914c6fb4d5253abf7fc46_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b0b02363c4c3e1518afab9d3a93bcc3f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;&#32;&#61;&#32;&#53;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"49\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3e9c4cc6ee8914c6fb4d5253abf7fc46_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> in general<\/li>\n<\/ol>\n<\/td>\n<td>32. Solve the formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2d180bb4d99b1834f643c35d43620b8e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#120;&#43;&#121;&#61;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"82\" style=\"vertical-align: -4px;\" \/> for y when<\/p>\n<ol style=\"list-style-type: lower-alpha\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-56f4f20a718bef81997b2e7fc8cb4c8f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"57\" style=\"vertical-align: 0px;\" \/><\/li>\n<li>in general<\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<tr>\n<td>33. Solve <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-fe4ca22b73e846ade2d79b174c7dc2ea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#56;&#48;&#61;&#97;&#43;&#98;&#43;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"118\" style=\"vertical-align: -2px;\" \/> for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3e9c4cc6ee8914c6fb4d5253abf7fc46_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<td>34. Solve <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e985e0efdbb2b282446fccd3a40795a1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#43;&#98;&#61;&#57;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"80\" style=\"vertical-align: -2px;\" \/> for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3e9c4cc6ee8914c6fb4d5253abf7fc46_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<\/tr>\n<tr>\n<td>35. Solve the formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f4d434b4de9b202d58337f0083c28f3e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#120;&#43;&#121;&#61;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"91\" style=\"vertical-align: -4px;\" \/> for y.<\/td>\n<td>36. Solve <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-fe4ca22b73e846ade2d79b174c7dc2ea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#56;&#48;&#61;&#97;&#43;&#98;&#43;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"118\" style=\"vertical-align: -2px;\" \/> for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-77479b59a494b611004da289deb0dfa3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<\/tr>\n<tr>\n<td>37. Solve the formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-83673b5b2a46dd7d4f7e5e25d6d423aa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#120;&#43;&#121;&#61;&#45;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"109\" style=\"vertical-align: -4px;\" \/> for y.<\/td>\n<td>38. Solve the formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3e2766587a16f1fc76444e25beb10109_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#120;&#43;&#121;&#61;&#49;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"92\" style=\"vertical-align: -4px;\" \/> for y.<\/td>\n<\/tr>\n<tr>\n<td>39. Solve the formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-5435ab26f27f81b778c5ed92c0331b70_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#120;&#43;&#51;&#121;&#61;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"91\" style=\"vertical-align: -4px;\" \/> for y.<\/td>\n<td>40. Solve the formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4ff1ff0a0e35c31cf972b8a727a85818_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;&#120;&#43;&#121;&#61;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"108\" style=\"vertical-align: -4px;\" \/> for y.<\/td>\n<\/tr>\n<tr>\n<td>41. Solve the formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-be900fdd6e4aecf5464cb33c5f86febf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#45;&#121;&#61;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"88\" style=\"vertical-align: -4px;\" \/> for y.<\/td>\n<td>42. Solve the formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-873e47c7488b1fda110888449fca3f55_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;&#43;&#50;&#121;&#61;&#49;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"99\" style=\"vertical-align: -4px;\" \/> for y.<\/td>\n<\/tr>\n<tr>\n<td>43. Solve the formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-0eb1eafa5e0c74c1197776ec8de1e08d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#80;&#61;&#50;&#76;&#43;&#50;&#87;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"108\" style=\"vertical-align: -2px;\" \/> for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2f1f6cda169436cf19561ee3f68a4351_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#76;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<td>44. Solve the formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-80d24fad1188c1dc4a7442a84221989f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#45;&#121;&#61;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"88\" style=\"vertical-align: -4px;\" \/> for y.<\/td>\n<\/tr>\n<tr>\n<td>45. Solve the formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2f0eabe3667aeaefb00802d6665f308e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#67;&#61;&#92;&#112;&#105;&#32;&#100;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"58\" style=\"vertical-align: 0px;\" \/> for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b8bfee3a85664394921a77e26dc3b4bb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#100;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<td>46. Solve the formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-0eb1eafa5e0c74c1197776ec8de1e08d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#80;&#61;&#50;&#76;&#43;&#50;&#87;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"108\" style=\"vertical-align: -2px;\" \/> for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9971a304ac6627e7f72c8fb3a3cf7961_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#87;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"19\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<\/tr>\n<tr>\n<td>47. Solve the formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-133ef62f492398b2f74dbf561d1d5b33_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#86;&#61;&#76;&#87;&#72;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"85\" style=\"vertical-align: 0px;\" \/> for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2f1f6cda169436cf19561ee3f68a4351_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#76;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<td>48. Solve the formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2f0eabe3667aeaefb00802d6665f308e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#67;&#61;&#92;&#112;&#105;&#32;&#100;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"58\" style=\"vertical-align: 0px;\" \/> for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4f79572098d6a611b29940572eb6ea64_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#105;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">49. Solve the formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-133ef62f492398b2f74dbf561d1d5b33_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#86;&#61;&#76;&#87;&#72;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"85\" style=\"vertical-align: 0px;\" \/> for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3059438fb9cf4559fb95848abc521278_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#72;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h3 data-type=\"title\">Everyday Math<\/h3>\n<table style=\"border-collapse: collapse;width: 100%\">\n<tbody>\n<tr>\n<td style=\"width: 51.0055%\">50.<strong data-effect=\"bold\"> Converting temperature.<\/strong> Yon was visiting the United States and he saw that the temperature in Seattle one day was 50<sup>o<\/sup> Fahrenheit. Solve for C in the formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4e209427831f434336bfc89ab0136c06_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#57;&#125;&#123;&#53;&#125;&#67;&#43;&#51;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"101\" style=\"vertical-align: -6px;\" \/> to find the Celsius temperature.<\/td>\n<td style=\"width: 48.9945%\">51.<strong data-effect=\"bold\"> Converting temperature.<\/strong> While on a tour in Greece, Tatyana saw that the temperature was 40<sup>o<\/sup> Celsius. Solve for F in the formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-034ac9a6f5b1afc6c70548cf795a7c55_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#67;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#57;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#70;&#45;&#51;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"118\" style=\"vertical-align: -6px;\" \/> to find the Fahrenheit temperature.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h3 data-type=\"title\">Writing Exercises<\/h3>\n<div id=\"fs-id1168345741424\" data-type=\"exercise\">\n<div id=\"fs-id1168345741426\" data-type=\"problem\">\n<table style=\"border-collapse: collapse;width: 100%\">\n<tbody>\n<tr>\n<td style=\"width: 50.0914%\">52. Solve the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-96845013aaba9878c53da9efb9a935ca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#120;&#45;&#50;&#121;&#61;&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"100\" style=\"vertical-align: -4px;\" \/> for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-bb53ce30a3ff5b6ca87fc6e1eb6588a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/><br \/>\na) when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-fdd2f48fde2b8b0544dd20ec76665796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"51\" style=\"vertical-align: -4px;\" \/><br \/>\nb) in general<br \/>\nc) Which solution is easier for you, a) or b)? Why?<\/td>\n<td style=\"width: 49.9086%\">53. Solve the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-730b527e3c5c7a7df9997a19c6a999d4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#43;&#51;&#121;&#61;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"91\" style=\"vertical-align: -4px;\" \/> for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-15f1a95c39a36eda2e95d509a5f0f8b9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/><br \/>\na) when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-56f4f20a718bef81997b2e7fc8cb4c8f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"57\" style=\"vertical-align: 0px;\" \/><br \/>\nb) in general<br \/>\nc) Which solution is easier for you, a) or b)? Why?<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<h1>Answers<\/h1>\n<table style=\"width: 100%\">\n<tbody>\n<tr>\n<td>1. 290 miles<\/td>\n<td>3. 30 miles<\/td>\n<td>5. 9 hr<\/td>\n<\/tr>\n<tr>\n<td>7. 7 hr<\/td>\n<td>9. 75 km\/hr<\/td>\n<td>11. 89 km\/hr<\/td>\n<\/tr>\n<tr>\n<td>13.<\/p>\n<ol type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d4092726bc77cbcd5657111998ba8137_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#116;&#61;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"39\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-56d6b9213dc41956731d0f2b1c4117e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#116;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#100;&#125;&#123;&#114;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"40\" style=\"vertical-align: -6px;\" \/><\/li>\n<\/ol>\n<\/td>\n<td>15.<\/p>\n<ol type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f2b69611a8586f41109f08daa94afd37_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#116;&#61;&#32;&#51;&#46;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"52\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-56d6b9213dc41956731d0f2b1c4117e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#116;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#100;&#125;&#123;&#114;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"40\" style=\"vertical-align: -6px;\" \/><\/li>\n<\/ol>\n<\/td>\n<td>17.<\/p>\n<ol type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-51b76df165094f1fd452f4675696c130_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#32;&#114;&#61;&#32;&#55;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"50\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-35c0548dc1be446c722971449129fd78_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#100;&#125;&#123;&#116;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"42\" style=\"vertical-align: -6px;\" \/><\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<tr>\n<td>19.<\/p>\n<ol style=\"list-style-type: lower-alpha\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2f6ef9098516d93df4d00c3df41fd393_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;&#61;&#32;&#52;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"50\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-35c0548dc1be446c722971449129fd78_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#100;&#125;&#123;&#116;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"42\" style=\"vertical-align: -6px;\" \/><\/li>\n<\/ol>\n<\/td>\n<td>21.<\/p>\n<ol style=\"list-style-type: lower-alpha\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-c5977590995c5ac49ade2d744a22c226_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#32;&#104;&#61;&#32;&#49;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"52\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b3fb72a1428034227993b2b9518df8f0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#104;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#65;&#125;&#123;&#98;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"54\" style=\"vertical-align: -6px;\" \/><\/li>\n<\/ol>\n<\/td>\n<td>23.<\/p>\n<ol style=\"list-style-type: lower-alpha\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b1c5dc9a0a551307b85dc0636d16eaca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#80;&#61;&#32;&#92;&#36;&#49;&#57;&#44;&#53;&#55;&#49;&#46;&#52;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"122\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-6f3bffecf4cd82fdc928768b3d708dd3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#80;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#73;&#125;&#123;&#114;&#116;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"51\" style=\"vertical-align: -6px;\" \/><\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<tr>\n<td>25.<\/p>\n<ol style=\"list-style-type: lower-alpha\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-fb353df324535ae1706d1d691e995bd1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#116;&#61;&#32;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"39\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-17b5a62cbe0bec65bb60260a2fbecdf9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#116;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#73;&#125;&#123;&#80;&#114;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"50\" style=\"vertical-align: -6px;\" \/><\/li>\n<\/ol>\n<\/td>\n<td>27.<\/p>\n<ol style=\"list-style-type: lower-alpha\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e7fcd722ca7030991aed319439742309_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#32;&#121;&#61;&#50;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"41\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d6b75ecd268fbe00a2336f3cc3271352_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#50;&#45;&#50;&#120;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"75\" style=\"vertical-align: -6px;\" \/><\/li>\n<\/ol>\n<\/td>\n<td>29.<\/p>\n<ol style=\"list-style-type: lower-alpha\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d46f116e170cbc50bc82dd36d7aa5d95_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#32;&#121;&#61;&#32;&#45;&#49;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"65\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-320bca873da3ff06685860fc6c3e5fe8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#55;&#43;&#51;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"96\" style=\"vertical-align: -4px;\" \/> or <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-83cd2c7d9c3e6c4906fde161fd801159_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#51;&#120;&#45;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"83\" style=\"vertical-align: -4px;\" \/><\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<tr>\n<td>31. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-83acd12724cc7e741f1b085097d851eb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/>; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2f32a50cf25416b4bee735d171599c05_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#61;&#32;&#57;&#48;&#45;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"80\" style=\"vertical-align: 0px;\" \/><\/td>\n<td>33. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-36599902533e1c7a5c6a18e2fe17dfc3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#61;&#32;&#49;&#56;&#48;&#45;&#98;&#45;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"119\" style=\"vertical-align: 0px;\" \/><\/td>\n<td>35. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-027c683a6fdec7506d986787fd3b9180_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#32;&#49;&#53;&#45;&#56;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"91\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>37. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-634a8a64186780da523eaffae0ebd198_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#32;&#52;&#120;&#45;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"83\" style=\"vertical-align: -4px;\" \/><\/td>\n<td>39. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-291bc61a2c4ac1b843c2c425cfc42147_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#45;&#52;&#120;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"68\" style=\"vertical-align: -6px;\" \/><\/td>\n<td>41. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-313fb9032f0db8980c1f9805f201fff4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#32;&#52;&#43;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"73\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>43. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-99733450a17a3f67f57d5cef90189fcf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#32;&#76;&#61;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#80;&#45;&#50;&#87;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"82\" style=\"vertical-align: -6px;\" \/><\/td>\n<td>45. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-6c567007808da9386d06d8190b240ef3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#100;&#61;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#67;&#125;&#123;&#92;&#112;&#105;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"46\" style=\"vertical-align: -6px;\" \/><\/td>\n<td>47. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3861511a28f9bb12d1a23e4ee0e90045_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#32;&#76;&#61;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#86;&#125;&#123;&#87;&#72;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"66\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>49. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-c7764be730edb24052396ccce7a20363_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#72;&#61;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#86;&#125;&#123;&#76;&#87;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"67\" style=\"vertical-align: -6px;\" \/><\/td>\n<td>51. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d7d942aee5a66f6d0726d699230ad870_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#61;&#32;&#49;&#48;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"64\" style=\"vertical-align: 0px;\" \/><sup>o<\/sup><\/td>\n<td>53. Answers will vary<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Attributions<\/h1>\n<p>This chapter has been adapted from \u201cSolve a Formula for a Specific Variable\u201d in <a href=\"https:\/\/openstax.org\/details\/books\/elementary-algebra\"><em>Elementary Algebra<\/em> (OpenStax)<\/a> by Lynn Marecek and MaryAnne Anthony-Smith, which is under a <a href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY 4.0 Licence<\/a>. Adapted by Izabela Mazur. See the Copyright page for more information.<\/p>\n","protected":false},"author":999,"menu_order":7,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[48],"contributor":[],"license":[],"class_list":["post-921","chapter","type-chapter","status-publish","hentry","chapter-type-numberless"],"part":398,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/pressbooks\/v2\/chapters\/921","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/wp\/v2\/users\/999"}],"version-history":[{"count":25,"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/pressbooks\/v2\/chapters\/921\/revisions"}],"predecessor-version":[{"id":2572,"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/pressbooks\/v2\/chapters\/921\/revisions\/2572"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/pressbooks\/v2\/parts\/398"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/pressbooks\/v2\/chapters\/921\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/wp\/v2\/media?parent=921"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/pressbooks\/v2\/chapter-type?post=921"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/wp\/v2\/contributor?post=921"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/wp\/v2\/license?post=921"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}