ACT Math : How to find proportion

Study concepts, example questions & explanations for ACT Math

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Example Questions

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Example Question #1 : How To Find Proportion

Max will be age X in 5 years. How old was he 4 years ago?

 

Possible Answers:

X – 9

X +5

X – 4

X – 5

Correct answer:

X – 9

Explanation:

Max will be X in 5 years. So today he is X -5 and 4 years ago he was (X-5)  - 4, that is X – 9.  It always helps to put numbers into the equations. Example: Max will be 12 in 5 years. How old was he 4 years ago? So today Max is 12 – 5 = 7.  Therefore, four years ago he was 7 -4 =3. Which is 12-5-4 =12-9 = 3

 

Example Question #2 : How To Find Proportion

If a pizza pie that has 16 slices and costs $12.00 is to be shared among 8 friends, how much should each person contribute?

 

Possible Answers:

$0.75

$1.75

$2

$1.50

Correct answer:

$1.50

Explanation:

It is $12 divided by 8 which is $1.50. The number of slices in the pizza pie is not relevant in this question.

 

Example Question #1 : How To Find Proportion

In a school relay race, every 5-man team must sprint 110 yards total.  However, Jim’s team is short a person.  Thus, Jim must run two sections for his team.  How far does Jim have to run?

 

Possible Answers:

22 yards

27.5 yards

44 yards

110 yards

45.4 yards

Correct answer:

44 yards

Explanation:

 We first find out how much each person must run.  Thus we take 110/5 to get 22 yards.  However, Jim must run twice the amount of a normal competitor, so we multiply by 2 to get 44 yards.

 

 

 

Example Question #4 : How To Find Proportion

A building that is 30 feet tall casts a shadow that is 50 feet long. If another building casts a shadow that is 100 feet long, how tall is the building?

Possible Answers:

600 feet

60 feet

167 feet

6 feet

1670 feet

Correct answer:

60 feet

Explanation:

This problem can be set up as a proportion: 30 feet/x feet = 50 feet/100 feet. To solve, we simply cross multiply: (30 feet * 100 feet) = (50 feet * x feet). Thus, 3000 feet = 50x feet. To solve for x, divide each side by 50. Therefore, = 60 feet.  If you got 167 feet, you may have set up the proportion incorrectly by mixing up the height of the building with the length of the shadow. If you got 6 feet or 600 feet, you may have made a computational error. If you got 1670 feet, you may have set the proportion up incorrectly and made a computational error.

 

Example Question #3 : How To Find Proportion

If a bicyclist can bike 24 miles per hour, how far (in miles) can he travel in 2 minutes, assuming he bikes at a constant speed (answer rounded to the nearest tenth)?

Possible Answers:

2.0

0.5

0.8

1.0

0.75

Correct answer:

0.8

Explanation:

0.8 mile.  Using some conversions:  ( (24mi/1hr)*(1hr/60min)*2min = 0.8 mile

Example Question #4 : How To Find Proportion

If 10,000 lbs of cement makes 85,000 lbs of concrete, how many pounds of concrete can be made with 3,000 pounds of cement?

Possible Answers:

30,000

25,500

10,000

363

12,230

Correct answer:

25,500

Explanation:

25,500 lbs of concrete. Setting up a ratio with x representing the number of pounds concrete the 3,000 of cement produces, we obtain the relation: (10,000/85,000) = (3,000/x), x = 25,500 pounds of concrete.

Example Question #5 : How To Find Proportion

There are 150 students in a lecture hall class in college. 12% of the students received an A. 20 students received a B. Twice the number of students who earned an A received a C. The remainder of the students received a D. Which grade did the students receive more than any other?

Possible Answers:

The students who got D's.

The students who got B's

The students who got A's.

The students who got C's

Cannot be determined. 

Correct answer:

The students who got D's.

Explanation:

First find 12% of 150, so 0.12 * 150 = 18 students received an A.

20 students received a B, and 36 students received a C (double the A's).

To find the number of D-grades, all we have to do is subtract these from the total (since there were no grades of F),

Thus: 150 – 18 – 20 – 36 = 76 students who received a D in the course, which is the most common grade.

Example Question #6 : How To Find Proportion

A brownie recipes calls for a 1:5 ratio of water to brownie mix. If you need 90 cups of brownie mix, how much water do you need? 

Possible Answers:

36 cups

6 cups

18 cups

25 cups

450 cups

Correct answer:

18 cups

Explanation:

First set up a proportion, 1/5 = x/90, then solve for x: 5x = 90 → x = 18 cups.

Example Question #7 : How To Find Proportion

If a 12 oz can of lemonade has 75 calories; how many calories are in an 8 oz can of lemonade?

Possible Answers:

65

50

70

60

55

Correct answer:

50

Explanation:

A proportion is a statement of equality between two fractions or two ratios. Set up a proportion between the size of the drink and the calories. To solve a proportion cross multiply and solve the resulting equation.

 

75/12 = x/8 → 150/24 = 3x/24 → 50/8 = x/8 → x = 50

Example Question #7 : How To Find Proportion

If there are 75 calories in a 6 oz glass of juice, how many calories will there be in an 8 oz glass?

Possible Answers:

Correct answer:

Explanation:

We set up a proportion:

 \frac{x}{75} = \frac{8}{6}  where = calories.

We cross multiply to get , so there will be 100 calories in 8 oz of juice.

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