# ACT Math : Proportion / Ratio / Rate

## Example Questions

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### Example Question #1 : How To Find The Volume Of A Solution

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= 1mL)?

100 mL

20 mL

50 mL

150 mL

25 mL

50 mL

Explanation:

The total volume is 5 * 5 * 4 = 100 cm. Half of this is 50 cmwhich is 50 mL.

### Example Question #2 : How To Find The Volume Of A Solution

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

Explanation:

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 : How To Find The Volume Of A Solution

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?

Explanation:

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 : How To Find The Volume Of A Solution

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.)

Explanation:

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 : How To Find The Volume Of A Solution

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?

Explanation:

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 : How To Find The Volume Of A Solution

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?

Explanation:

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 : Proportion / Ratio / Rate

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?

3:1

20:3

27:10

3:5

14:5

27:10

Explanation:

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 #1441 : Act Math

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

1 : 9

50 : 5

1 : 5

5 : 50

9 : 1

9 : 1

Explanation:

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 #1 : Proportion / Ratio / Rate

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

What is the ratio of green marbles to blue marbles?

Explanation:

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 #18 : Proportion / Ratio / Rate

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?

Explanation:

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 .

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