### All ACT Math Resources

## Example Questions

### 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 – 5

X – 4

X +5

X – 9

**Correct answer:**

X – 9

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

$1.50

$2

$1.75

**Correct answer:**

$1.50

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 #3 : 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:**

110 yards

27.5 yards

22 yards

45.4 yards

44 yards

**Correct answer:**

44 yards

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 #44 : Proportion / Ratio / Rate

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:**

60 feet

6 feet

1670 feet

600 feet

167 feet

**Correct answer:**

60 feet

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 = 50*x* feet. To solve for *x*, divide each side by 50. Therefore, *x *= 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 #4 : 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:**

0.75

2.0

0.5

0.8

1.0

**Correct answer:**

0.8

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

### Example Question #5 : 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

12,230

363

**Correct answer:**

25,500

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 #6 : 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:**

Cannot be determined.

The students who got C's

The students who got D's.

The students who got A's.

The students who got B's

**Correct answer:**

The students who got D's.

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 #7 : 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:**

25 cups

18 cups

450 cups

36 cups

6 cups

**Correct answer:**

18 cups

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

### Example Question #8 : 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

60

70

50

55

**Correct answer:**

50

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 #9 : 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:**

We set up a proportion:

where = calories.

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

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