3.5 Chapter Review

Review Exercises

Write a Ratio as a Fraction

In the following exercises, write each ratio as a fraction. Simplify the answer if possible.

1. 56 to 32 2. 28 to 40
3. 1.2 to 1.8 4. 3.5 to 0.5
5. 2\frac{1}{3}\phantom{\rule{0.2em}{0ex}}\text{to}\phantom{\rule{0.2em}{0ex}}5\frac{1}{4} 6. 1\frac{3}{4}\phantom{\rule{0.2em}{0ex}}\text{to}\phantom{\rule{0.2em}{0ex}}1\frac{5}{8}
7. 28 inches to 3 feet 8. 64 ounces to 30 ounces

Write a Rate as a Fraction

In the following exercises, write each rate as a fraction. Simplify the answer if possible.

9. 90 pounds per 7.5 square inches 10. 180 calories per 8 ounces
11.\text{\$612.50} for 35 hours 12. 126 miles in 4 hours

Find Unit Rates

In the following exercises, find the unit rate.

13. 90 pounds per 7.5 square inches 14. 180 calories per 8 ounces
15. \text{\$612.50} for 35 hours 16. 126 miles in 4 hours

Find Unit Price

In the following exercises, find the unit price.

17.Highlighters: 6 for \text{\$2.52} 18. T-shirts: 3 for \text{\$8.97}
19. Anna bought a pack of 8 kitchen towels for \text{\$13.20}. How much did each towel cost? Round to the nearest cent if necessary. 20. An office supply store sells a box of pens for \text{\$11}. The box contains 12 pens. How much does each pen cost?
In the following exercises, find each unit price and then determine the better buy.
21.Vitamins: 60 tablets for \text{\$6.49} or 100 for \text{\$11.99}? 22. Shampoo: 12 ounces for \text{\$4.29} or 22 ounces for \text{\$7.29}?

Translate Phrases to Expressions with Fractions

In the following exercises, translate the English phrase into an algebraic expression.

23. a adults to 45 children 24. 535 miles per h\phantom{\rule{0.2em}{0ex}}\text{hours}
25. the ratio of 19 and the sum of 3 and n 26. the ratio of 4y and the difference of x and 10

In the following exercises, write each percent as a ratio.

27. \text{32\%} admission rate for the university 28. \text{53.3\%} rate of college students with student loans

In the following exercises, write as a ratio and then as a percent.

29. 13 out of 100 architects are women. 30. 9 out of every 100 nurses are men.

In the following exercises, convert each percent to a fraction.

31. \text{48\%} 32. \text{175\%}
33. \text{64.1\%} 34. 8\frac{1}{4}\%

In the following exercises, convert each percent to a decimal.

35. \text{6\%} 36. \text{23\%}
37. \text{128\%} 38. 4.9%

In the following exercises, convert each percent to a) a simplified fraction and b) a decimal.

39. In 2016,\text{17\%} of the Canadian population was age 65 or over. (Source: www12.statcan.gc.ca) 40. In 2016,\text{16.6\%} of the Canadian population was under 15 years old. (Source: www12.statcan.gc.ca)
41. When a die is tossed, the probability it will land with an even number of dots on the top side is \text{50\%}. 42. A couple plans to have three children. The probability they will all be girls is \text{12.5\%}.

In the following exercises, convert each decimal to a percent.

43. 0.04 44. 0.15
45. 2.82 46. 3
47. 0.003 48. 1.395

In the following exercises, convert each fraction to a percent.

49. \frac{3}{4} 50. \frac{11}{5}
51. 3\frac{5}{8} 52. \frac{2}{9}
53. According to the Centers for Disease Control, \frac{2}{5} of adults do not take a vitamin or supplement. 54. According to the Centers for Disease Control, among adults who do take a vitamin or supplement, \frac{3}{4} take a multivitamin.

In the following exercises, translate and solve.

55. What number is \text{46\%} of 350? 56. \text{120\%} of 55 is what number?
57. 84 is \text{35\%} of what number? 58. 15 is \text{8\%} of what number?
59. \text{200\%} of what number is 50? 60. \text{7.9\%} of what number is \text{\$4.74}?
61. What percent of 120 is 81.6? 62. What percent of 340 is 595?

Solve General Applications of Percents

In the following exercises, solve.

63. When Aurelio and his family ate dinner at a restaurant, the bill was \text{\$83.50}. Aurelio wants to leave \text{20\%} of the total bill as a tip. How much should the tip be? 64. One granola bar has 2 grams of fiber, which is \text{8\%} of the recommended daily amount. What is the total recommended daily amount of fiber?
65. The nutrition label on a package of granola bars says that each granola bar has 190 calories, and 54 calories are from fat. What percent of the total calories is from fat? 66. Elsa gets paid \text{\$4,600} per month. Her car payment is \text{\$253}. What percent of her monthly pay goes to her car payment?
67. Marta got a gift of \text{\$1900} from her uncle. She spent \text{35\%} of that money for her trip to Victoria. How much money she has left?. 68. Last year Bernard bought a new car for \text{\$30,000}. If the value of the car depreciated \text{20\%} every year , find the value of the car this year.

Solve Proportions and their Applications

In the following exercises, write each sentence as a proportion.

69. 3 is to 8 as 12 is to 32. 70. 95 miles to 3 gallons is the same as 475 miles to 15 gallons.
71. 1 teacher to 18 students is the same as 23 teachers to 414 students. 72. \text{\$7.35} for 15 ounces is the same as \text{\$2.94} for 6 ounces.

In the following exercises, determine whether each equation is a proportion.

73. \frac{5}{13}=\frac{30}{78} 74. \frac{16}{7}=\frac{48}{23}
75. \frac{12}{18}=\frac{6.99}{10.99} 76. \frac{11.6}{9.2}=\frac{37.12}{29.44}

In the following exercises, solve each proportion.

77. \frac{x}{36}=\frac{5}{9} 78. \frac{7}{a}=\frac{-6}{84}
79. \frac{1.2}{1.8}=\frac{d}{6} 80. \frac{\frac{1}{2}}{2}=\frac{m}{20}

In the following exercises, solve the proportion problem.

81. The children’s dosage of acetaminophen is 5 millilitre s (ml) for every 25 pounds of a child’s weight. How many millilitre s of acetaminophen will be prescribed for a 60 pound child? 82. After a workout, Dennis takes his pulse for 10 sec and counts 21 beats. How many beats per minute is this?
83. An 8 ounce serving of ice cream has 272 calories. If Lavonne eats 10 ounces of ice cream, how many calories does she get? 84. Alma is going to Europe and wants to exchange \text{\$1,200} into Euros. If each dollar is 0.65 Euros, how many Euros will Alma get?
85. Zack wants to drive from Abbotsford to Banff, a distance of 494 miles. If his car gets 38 miles to the gallon, how many gallons of gas will Zack need to get to Banff? 86. Teresa is planning a party for 100 people. Each gallon of punch will serve 18 people. How many gallons of punch will she need?

In the following exercises, translate to a proportion.

87. What number is \text{62\%} of 395? 88. 42 is \text{70\%} of what number?
89. What percent of 1,000 is 15? 90. What percent of 140 is 210?

In the following exercises, translate and solve using proportions.

91. What number is \text{85\%} of 900? 92. \text{6\%} of what number is \text{\$24}?
93. \text{\$3.51} is \text{4.5\%} of what number? 94. What percent of 3,100 is 930?

In the following exercises, convert each percent to a) a decimal b) a simplified fraction.

95. \text{24\%} 96. \text{5\%}
97. \text{350\%}

In the following exercises, convert each fraction to a percent. (Round to 3 decimal places if needed.)

98. \frac{7}{8} 99. \frac{1}{3}
100. \frac{11}{12}

In the following exercises, solve the percent problem.

101. 65 is what percent of 260? 102. What number is \text{27\%} of 3,000?
103. \text{150\%} of what number is 60? 104. Write as a proportion: 4 gallons to 144 miles is the same as 10 gallons to 360 miles.
105. Vin read 10 pages of a book in 12 minutes. At that rate, how long will it take him to read 35 pages?

Review Answers

1. \frac{7}{4} 3. \frac{2}{3} 5. \frac{4}{9}
7. \frac{7}{9} 9. \frac{90\phantom{\rule{0.2em}{0ex}}\text{pounds}}{7.5\phantom{\rule{0.2em}{0ex}}\text{square inches}} 11. \frac{\text{\$612.50}}{35\phantom{\rule{0.2em}{0ex}}\text{hours}}
13. 12 pounds/sq.in. 15. $17.50/hour 17. $0.42
19. $1.65 21. $0.11, $0.12; 60 tablets for $6.49 23. \frac{a\phantom{\rule{0.2em}{0ex}}\text{adults}}{45\phantom{\rule{0.2em}{0ex}}\text{children}}
25. \frac{19}{3+n} 27. \frac{32}{100} 29. \frac{13}{100},\text{13\%}
31. \frac{12}{25} 33. \frac{641}{1000} 35. 0.06
37. 1.28 39.

a) \phantom{\rule{0.2em}{0ex}}\frac{17}{100}

b) \phantom{\rule{0.2em}{0ex}}0.17

41.

a) \phantom{\rule{0.2em}{0ex}}\frac{1}{2}

b) \phantom{\rule{0.2em}{0ex}}0.5

43. 4% 45. 282% 47. 0.3%
49. 75% 51. 362.5% 53. 40%
55. 161 57. 240 59. 25
61. 68% 63. $16.70 65. 28.4%
67. 1235 69. \frac{3}{8}=\frac{12}{32} 71. \frac{1}{18}=\frac{23}{414}
73. yes 75. no 77. 20
79. 4 81. 12 83. 340
87. \frac{x}{395}=\frac{62}{100} 89. \frac{x}{100}=\frac{15}{1000} 91.765
93. $78 95.0.24,\frac{6}{25} 97. 3.5,3\frac{1}{2}
99. 33.333% 101.25% 103. 40
105. 42

Chapter Test

1. Write a ratio as a fraction. Simplify the answer if possible. 42 to 28

2. Write a rate as a fraction. Simplify the answer if possible. 80 pounds per 6.5 square inches

3. Find the unit rate. \text{\$868.80} for 24 hours 4. Marta bought a pack of 6 paint brushes for \text{\$32.20}. How much did each brush cost? Round to the nearest cent if necessary
5. Find each unit price and then the better buy.
Laundry detergent: 64 ounces for \text{\$10.99} or 48 ounces for \text{\$8.49}
6. Convert a percent to a fraction: \text{245\%}
7. Convert a decimal to a percent: 0.07 8. Convert a fraction to a percent. (Round to 3 decimal places if needed.) \frac{11}{8}
9. What number is \text{36\%} of 450? 10. \text{8\%} of what number is \text{\$34}?
11. 57.6 is what percent of 360? 12. One granola bar has 3 grams of fiber, which is \text{12\%} of the recommended daily amount. What is the total recommended daily amount of fiber?
13. Klaudia is going to Poland and wants to exchange \text{\$1,400} into Polish zlotych. If each dollar is 2.91 zlotych, how many zlotych will Klaudia get? 14. Solve a proportion:\frac{24}{x}=\frac{3}{7}
15. Solve a proportion:\frac{x}{6}=\frac{9}{24} 16.Solve a proportion:\frac{2.4}{1.6}=\frac{t}{6.2}

Test Answers

1. \frac{3}{2} 2. \frac{160}{13} 3. $36.20
4. $5.37 5. 64 ounces for $10.99 is the better buy 6. \frac{49}{20}
7. 7% 8. 137.5% 9. 162
10. 425 11. 16% 12. 25 grams
13. 4074 zlotych 14. 56 15. 2.25
16. 9.3

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Intermediate Algebra I Copyright © 2021 by Pooja Gupta is licensed under a Creative Commons Attribution 4.0 International License, except where otherwise noted.

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