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

By Dr. Janet E. Wall
McGraw-Hill Professional

### Motion

Motion problems deal with how long it will take to get from point a to point b if you are traveling at a certain steady rate. To solve them, use this formula:

Distance = rate × time
d = rt

Example

If a racing boat travels at a steady rate of 80 miles per hour, how many miles could it travel in 3.5 hours?

Procedure

• What must you find? Distance traveled in 3.5 hours
• What are the units? Miles
• What do you know? Rate = 80 miles per hour; time = 3.5 hours
• Create an equation and solve.
• d = rt

Substitute values into the formula:

d = (80)(3.5)

d = 280 miles

### Percent

There are likely to be word problems involving percent on both the Arithmetic Reasoning and Math Knowledge tests of the ASVAB.

Example 1

Lilly's bill at a restaurant is \$22.00, and she wants to leave a 15% tip. How much money should her tip be?

Procedure

• What must you find? Amount of tip
• What are the units? Dollars and cents
• What do you know? Total bill = \$22.00; Percent of tip = 15
• Create an equation and solve.
• Tip = 15% × 22.00

Substitute and solve.

t = (0.15)(22.00)

t = \$3.30

Example 2

Frederick earns \$1,500 per month at his job, but 28% of that amount is deducted for taxes. What is his monthly take-home pay?

Procedure

• What must you find? Monthly take-home pay
• What are the units? Dollars and cents
• What do you know? Monthly pay before taxes = \$1,500; percent deducted = 28%
• Create an equation and solve.

Take-home pay is 1,500 minus 28% × 1,500.

T = 1,500 – (1,500 × 0.28)

T = 1,500 – (420)

T = \$1080

Example 3

40 is 80% of what number?

Procedure:

• What must you find? Number of which 40 is 80%
• What are the units? Numbers
• What do you know? 40 is 80% of some larger number

Create an equation and solve.

### 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.

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