Ratios, Proportions, Percentages, Fractions

Proportions & Ratios

1. Marcus's favorite casserole recipe requires 3 eggs and makes 6 servings. Marcus will modify the recipe by using 5 eggs and increasing all other ingredients in the recipe proportionally. What is the total number of servings the modified recipe will make?

2017 April(74F) Math Question 1

2013 December(71E) Math Question 1

1. A cookie recipe that yields 24 cookies requires 1 3/4 cups of butter, When the ingredients in this recipe are increased proportionally, how many cups of butter are required for the recipe to yield 72 cookies?

2016 April(72E) Math Question 1

2010 December(69A) Math Question 2

2009 June(67C) Math Question 3

3. Last year at RT University, the ratio of the number of students accepted to the number of students applying for admission was 2 to 7. RT University accepted 630 students last year. Flow many students applied to RT University last year?

2018 April(A09) Math Question 3

2011 April(67F) Math Question 3

2012 June(70C) Math Question 4

4. Given that 5 pounds of coffee makes exactly 210 servings, how many pounds of coffee makes exactly 70 servings?

Ratios

2021 April(D05) Math Question 4

2012 December(71A) Math Question 5

2010 June(68C) Math Question 5

2020 July(C01) Math Question 6

2018 April(A09) Math Question 7

7. On a map, 1/2 inch represents 10 actual miles. Two

2016 December(74H) Math Question 7

2009 April(66F) Math Question 8

9. In a poll of 500 registered voters, 337 voters favored a proposal to increase funding for local schools. Suppose the poll is indicative of how the 22,000 registered voters will vote on the proposal. Which of the following values is closest to how many of the 22,000 registered voters will be expected to vote in favor of the proposal?

2018 June(A11) Math Question 9

2019 December(C03) Math Question 9

2019 June(72F) Math Question 9

2012 June(70C) Math Question 9

9. According to the United States Department of Commerce, the approximate area of Rhode Island is 1.5 × 103 square miles and the approximate area of Alaska is 6.6 × 105 square miles. Using these measurements, which of the following is closest to the ratio of the area of Alaska to the area of Rhode Island?

Scientific Notation

2021 April(D05) Math Question 9

10. Katerina runs 15 miles in 2 1/2 hours. What is the average number of minutes it takes her to run 1 mile?

Speed, Distance, and Time

Unit Conversions (Feet to inches, miles to feet, hours to seconds)

2021 April(Z04) Math Question 10

12. The ratio of 30 to 24 is the same as the ratio of 40 to what number?

2014 December(72G) Math Question 12

13. Jake wants to build a scale model of his house. The house is 48 feet long and 32 feet wide, and it is 30 feet tall at the highest point. Jake wants the model to be 8 inches long. How wide, in inches, should his model be?

Rectangular solids

2021 April(D05) Math Question 13

15. The ratio of Jane’s age to her daughter’s age is 9:2. The sum of their ages is 44. How old is Jane?

2017 June(74C) Math Question 15

2021 April(Z04) Math Question 15

16. Chelsea’s car travels an average of 32 miles per gallon of gas used, and she pays an average of $2.25 per gallon of gas. Chelsea will drive her car along Highway H from Marville to Bright City. To the nearest $1, what will be the total cost of gas that her car uses for the drive?

2014 April(71H) Math Question 16

16. In this survey, what is the ratio of the number of students who selected Athletics to the number of students who selected Soccer?

2013 June(71C) Math Question 16

2013 December(71E) Math Question 16

17. What value of x makes the proportion below true?

2017 June(74C) Math Question 17

20. A survey about 3 issues affecting Bluff City Park was given to 60 residents. The results of the survey are shown below.

2016 December(74H) Math Question 20

2013 April(71G) Math Question 20

2019 December(C03) Math Question 21

2013 April(71G) Math Question 21

23. Maranda is going to a leadership conference and was given the map below to guide her to the Conference Center. The map has no scale, but she knows that the distance between Exits 77 and 79 on Interstate 29 is 2 miles. On the map, this distance is of an inch. She plans to exit Interstate 29 at Exit 77, travel on 41st Street to Cliff Avenue, and then proceed on Cliff Avenue to the Conference Center. The distance on the map from Exit 77 to the Conference Center over this route is 3 inches. What is this distance, in miles?

2020 December(D03) Math Question 23

2013 April(71G) Math Question 24

2011 June(69F) Math Question 25

25. The Department of Natural Resources  (DNR) is estimating the deer population in Twin Pines County. Several months ago, DNR  rangers captured, tagged, and then released 108 deer. Recently, DNR rangers captured 54 deer in the county and found that 36  of them had been tagged in the earlier capture. The DNR estimates the deer population in the county using the proportion below. What is the DNR estimate of the deer population in the county?

2021 December(E23) Math Question 25

2020 July(C01) Math Question 27

29. Points A, B, C, and D lie on the real number line as shown below. The coordinate of B is 0, AC is 15 units long, BD is 20 units long, and AD is 32 units long. What is the coordinate of C ?

2014 December(72G) Math Question 29

31. The Wilson family sold a shipment of walnuts to a farming cooperative for $210 at the rate of $0.03 per pound. If their shipment averaged 12 walnuts per pound, which of the following is closeAt to the total number of walnuts in the shipment? •

2013 June(71C) Math Question 31

2019 April(B04) Math Question 32

2018 December(B05) Math Question 32

2018 December(B05) Math Question 33

34. A school admissions office accepts 2 out of every 7 applicants. Given that the school accepted 630 students, how many applicants were NOT accepted?

2017 June(74C) Math Question 34

2018 December(B05) Math Question 34

2010 April(68G) Math Question 35

2009 June(67C) Math Question 35

35. Anoki made a scale drawing of his rectangular classroom. The classroom is 7.5 meters by 9.0 meters. In his scale drawing, Anoki made the length of the shorter side of the classroom 9.0 centimeters. What is the length, in centimeters, of the longer side of the classroom in Anoki’s scale drawing?

2021 June(D06) Math Question 35

2014 April(71H) Math Question 41

2013 December(71E) Math Question 42

2013 April(71G) Math Question 42

42. The couple will consider the price per square foot of each condo. Let x and y be the price per square foot, rounded to the nearest $1, of Condo X and Condo Y, respectively. One of the following comparisons is true. Which one?

2021 June(D06) Math Question 42

45. Given that x = 2 when y = 12 for the proportion x/6 = k/y, what is x when y = 8 ?

2014 December(72G) Math Question 45

2012 June(70C) Math Question 46

46. Diana is baking bread, and the original recipe calls for 1 1/2 teaspoons of yeast and 2 1/2 cups of flour. Diana will use the entire contents of a packet that contains 2 1/4 teaspoons of yeast and will use the same ratio of ingredients called for in the original recipe. How many cups of flour will Diana use?

2015 June(73C) Math Question 46

51. Twelve jurors are needed for an upcoming trial. The diagram below illustrates a part of the process of jury selection. The 12 jurors will be selected from a jury pool of about 60 people. The court records show a trend that only 40% of the people who are summoned for jury duty actually appear and that of the people who appear, are excused. If this same trend continues, how many people should be summoned to have as close as possible to 60 people in the jury pool?

Percentage Increase / Decrease

2021 April(Z04) Math Question 51

51. Joe, Carmen, and Dave each receive an allowance. The ratio of Joe’s allowance to Dave’s allowance is 3:2, and the ratio of Dave’s allowance to Carmen’s allowance is 3:4. What is the ratio of Joe’s allowance to Carmen’s allowance?

2020 December(D03) Math Question 51

55. The ratio of Alani’s height to Baahir’s height is 5:7. The ratio of Baahir’s height to Connor’s height is 4:3. What is the ratio of Alani’s height to Connor’s height?

2018 June(A11) Math Question 55

2018 December(B05) Math Question 55

55. The right triangle shown below is 8 squares high and 10 squares long. One of the following values is the ratio of the shaded area to the unshaded area. Which one?

2021 December(E23) Math Question 55

57. The ratio of a to b is 6 to 1,  and the ratio of b to c is
12 to 1. What is the value of  (2a+3b)/(4b+3c) ?

2019 June(B02) Math Question 57

57. One day on the New York Currency Exchange, 1 British pound (£1) could be exchanged for $2.75 in U.S. currency, and 1  Canadian dollar ($1) could be exchanged for $0.92 in U.S. currency. On that day, how much Canadian currency, rounded to the nearest Canadian cent, could be exchanged for £2 ?

2021 December(E23) Math Question 57

60. Tameka calculates that she needs 360 square feet of new carpet. But the type of carpet that she wants is priced by the square yard. How many square yards of carpet does she need?

Proportions & RatiosRatios, Proportions, Percentages, FractionsACT math questions

2017 April(74F) Math Question 1

2013 December(71E) Math Question 1