### All ACT Math Resources

## Example Questions

### Example Question #1 : Proportion / Ratio / Rate

A rectangular container holds a liquid. The dimensions of the container are 5 cm by 5 cm by 4 cm. If the container is half full, how much liquid is in the container (1 cm^{3 }= 1mL)?

**Possible Answers:**

150 mL

20 mL

100 mL

50 mL

25 mL

**Correct answer:**

50 mL

The total volume is 5 * 5 * 4 = 100 cm^{3 }. Half of this is 50 cm^{3 }which is 50 mL.

### Example Question #2 : Proportion / Ratio / Rate

A dog eats treats in days. At this rate, how many treats does the dog eat in days?

**Possible Answers:**

**Correct answer:**

This is a rate problem. We need to first find out how many treats a day the dog eats. Then to find the number of treats the dog eats in days, we multiply the number of days by the number of treats a day the dog eats.

From the given information, we know that the dog eats treats a day.

Then we multiply that number by the number of days.

Now simplify.

### Example Question #3 : Proportion / Ratio / Rate

One serving of party drink is comprised of of syrup, of water, and of apple juice. If a large bowl of the drink contains of apple juice, how much of the total drink is in the bowl?

**Possible Answers:**

**Correct answer:**

The total drink is made up of . Therefore, for a problem like this, you can set up a ratio:

First, simplify the right side of the equation:

Next, solve for :

. Therefore, the total amount of drink is .

### Example Question #4 : Proportion / Ratio / Rate

There is a coffee drink made of of coffee, of milk, of cream, and of flavoring. If you have an unlimited amount of flavoring and milk but only of cream and of coffee, how many ounces of drink can you make? (Presume that you cannot make partial servings.)

**Possible Answers:**

**Correct answer:**

To begin with, you need to compute what is going to be your limiting factor. For the cream, you can make:

servings.

For the coffee, you can make:

servings.

Therefore, this second value is your total number of servings. (You must choose the minimum, for it will be what limits your beverage-making.)

So, you know that each drink is . If you can make servings (remember, no partial servings!), you can make a total of .

### Example Question #5 : Proportion / Ratio / Rate

A drink is made up of orange juice to carbonated water. If a bowl of this drink contains of carbonated water, how many total cups of the drink are there in the bowl?

**Possible Answers:**

**Correct answer:**

To start this, you can set up a proportion as follows:

, where is the number of cups of orange juice.

Now, solving for , you get:

Be careful, though! This means that the total solution is actually or .

### Example Question #6 : Proportion / Ratio / Rate

A solution has of solution X and of solution Y. If you wanted a solution containing of solution Y, how much total solution would you need?

**Possible Answers:**

**Correct answer:**

To start, notice that the ratio of solution X to solution Y is:

Based on the quesiton, you know that you are looking for a certain amount of solution X based on a given amount of solution Y. Thus, for your data, you know:

Solving for X, you get:

This is the total amount of solution X that you will need to keep the ratios correct. Do not forget that you need to have a *total* solution amount, thus add this amount of solution X to solution Y's amount, thus giving you:

or

### Example Question #1 : How To Find A Ratio

The ratio of a to b is 9:2, and the ratio of c to b is 5:3. What is the ratio of a to c?

**Possible Answers:**

3:5

3:1

20:3

27:10

14:5

**Correct answer:**

27:10

Set up the proportions a/b = 9/2 and c/b = 5/3 and cross multiply.

2a = 9b and 3c = 5b.

Next, substitute the b’s in order to express a and c in terms of each other.

10a = 45b and 27c = 45b **-->** 10a = 27c

Lastly, reverse cross multiply to get a and c back into a proportion.

a/c = 27/10

### Example Question #2 : How To Find A Ratio

There is a shipment of 50 radios; 5 of them are defective; what is the ratio of non-defective to defective?

**Possible Answers:**

50 : 5

1 : 9

9 : 1

5 : 50

1 : 5

**Correct answer:**

9 : 1

Since there are 5 defective radios, there are 45 nondefective radios; therefore, the ratio of non-defective to defective is 45 : 5, or 9 : 1.

### Example Question #3 : How To Find A Ratio

A bag contains 3 green marbles, 5 red marbles, and 9 blue marbles.

What is the ratio of green marbles to blue marbles?

**Possible Answers:**

**Correct answer:**

The ratio of green to blue is .

Without simplifying, the ratio of green to blue is (order does matter).

Since 3 and 9 are both divisible by 3, this ratio can be simplified to .

### Example Question #4 : How To Find A Ratio

A small company's workforce consists of store employees, store managers, and corporate managers in the ratio 10:3:1. How many employees are either corporate managers or store managers if the company has a total of employees?

**Possible Answers:**

**Correct answer:**

Let be the number of store employees, the number of store managers, and the number of corporate managers.

, so the number of store employees is .

, so the number of store managers is .

, so the number of corporate managers is .

Therefore, the number of employees who are either store managers or corporate managers is **.**