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# Arithmetic Word Problems Study Guide for McGraw-Hill's ASVAB (page 3)

By — McGraw-Hill Professional
Updated on Jun 26, 2011

### 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

2x = 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 + 2x = 150

3x = 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.

2x = 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

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