### Percent Change

Some ASVAB word problems ask you to calculate the percent change from one number or amount to another.

*Example 1 *

Samantha now earns $300 per month working at a cosmetics store, but starting next month her monthly salary will be $375. Her new salary will be what percent increase over her current salary?

*Procedure*

*What must you find?*Percent change from current salary*What are the units?*Percent*What do you know?*Current pay = $300/month; pay after the raise = $375/month*Create an equation and solve.*

Substitute values and solve:

**Example 2**

On his sixteenth birthday, Brad was 60 inches tall.

On his seventeenth birthday, he was 65 inches tall. What was the percent increase in Brad's height during the year?

*Procedure*

*What must you find?*Percent change in height*What are the units?*Percent*What do you know?*Starting height = 60 inches; height after a year = 65 inches*Create an equation and solve.*

Substitute values and solve.

**Example 3**

At a certain store, every item is discounted by 15% off the original price. If Kevin buys a CD originally priced at $15.00 and a baseball cap originally priced at $11.50, how much money will he save?

*Procedure*

*What must you find?*Total amount saved*What are the units?*Dollars and cents*What do you know?*Percent change = 15%; original price for two items = $15.00 + $11.50 = $26.50*Create an equation and solve.*

Substitute values and solve.

### Numbers and Number Relationships

Pay attention to the key words in this type of word problem.

*Example 1 *

If the sum of two numbers is 45 and one number is 5 more than the other, what are the two numbers?

*Procedure*

*What must you find?*Value of each number*What are the units?*Numbers*What do you know?*Sum of two numbers is 45; one number is 5 more than the other*Create an equation and solve.*

Let *x* be the smaller number.

*x* + (*x* + 5) = 45

Solve for *x*:

*x* + *x* + 5 = 45

2*x* = 40

*x* = 20

So the two numbers are 20 and 20 + 5 = 25.

**Example 2**

One number is twice the size of another, and the two numbers together total 150. What are the two numbers?

*Procedure*

*What must you find?*Value of each number*What are the units?*Numbers*What do you know?*One number is twice the size of the other, and the sum of the numbers is 150.*Create an equation and solve.*

Let *x* be the smaller number.

*x* + 2*x* = 150

3*x* = 150

*x* = 50

So the smaller number is 50 and the larger number is 100.

### Age

Some word problems ask you to calculate a person's age given certain facts.

*Examples*

Jessica is 26 years old. Two years ago she was twice as old as her brother Ned. How old is Ned now?

*Procedure*

*What must you find?*Ned's age now*What are the units?*Years*What do you know?*When Jessica was 24, she was 2 times as old as Ned*Create an equation and solve.*

Prepare an equation that shows the relationship.

Let *x* = Ned's age two years ago.

2*x* = 24

*x* = 12

Ned's age two years later = 12 + 2 = 14 years

### Measurement

Some word problems will ask you to use what you know about units of measure to solve problems.

*Example*

How many cups of milk are in 5 pints of milk?

*Procedure*

*What must you find?*The number of cups of milk in 5 pints*What are the units?*Cups*What do you know?*According to the chart in Chapter 8, there are 2 cups in 1 pint.*Create an equation and solve.*

Let *x* = the number of cups in 5 pints.

1 pint = 2 cups

5 × 1 pint = 5 × 2 cups (Multiply both sides of the equation by 5)

5 pints = 10 cups = *x* cups

*x* = 10

So there are 10 cups in 5 pints.

Practice questions for this study guide can be found at:

Arithmetic Word Problems Practice Problems for McGraw-Hill's ASVAB