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# Percents for Firefighter Exam Study Guide (page 2)

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Updated on Jul 5, 2011

### Percent Word Problems

Word problems involving percents come in three main varieties:

• Find a percent of a whole.
Example: What is 30% of 40?
• Find what percent one number is of another number.
Example: 12 is what percent of 40?
• Find the whole when the percent of it is given.
Example: 12 is 30% of what number?

Although each variety has its own approach, there is a single shortcut formula you can use to solve each of these:

The is is the number that usually follows or is just before the word is in the question.

The of is the number that usually follows the word of in the question.

The % is the number that is in front of the % or percent in the question.

Or you may think of the shortcut formula as:

To solve each of the three varieties, we are going to use the fact that the cross-products are equal. The cross-products are the products of the numbers diagonally across from each other. Remembering that product means multiply, here's how to create the cross-products for the percent shortcut:

part × 100 = whole × %

Here's how to use the shortcut with cross-products:

• Find a percent of a whole.
What is 30% of 40?
30 is the % and 40 is the of number:
Cross-multiply and solve for is:                 is × 100 = 40 × 30
is × 100 = 1,200
12 × 100 = 1,200
Thus, 12 is 30% of 40.
• Find what percent one number is of another number.
12 is what percent of 40?
12 is the is number and 40 is the of number:
Cross-multiply and solve for %:                           12 × 100 = 40 × %
1,200 = 40 × %
1,200 = 40 × 30
Thus, 12 is 30% of 40.
• Find the whole when the percent of it is given.
12 is 30% of what number?
12 is the is number and 30 is the %:
Cross-multiply and solve for the of number:         12 × 100 = of × 30
1,200 = of × 30
1,200 = 40 × 30
Thus, 12 is 30% of 40.

You can use the same technique to find the percent increase or decrease. The is number is the actual increase or decrease, and the of number is the original amount.

Example: If a merchant puts his \$20 hats on sale for \$15, by what percent does he decrease the selling price?
1. Calculate the decrease, the is number:                         \$20 – \$15 = \$5
2. The of number is the original amount, \$20
3. Set up the equation and solve for of by cross-multiplying:
5 × 100 = 20 × %
500 = 20 × %
500 = 20 × 25
4. Thus, the selling price is decreased by 25%.
If the merchant later raises the price of the hats from \$15 back to \$20,
don't be fooled into thinking that the percent increase is also 25%! It's             5 × 100 = 15 × %
actually more, because the increase amount of \$5 is now based on a lower     500 = 15 × %
original price of only \$15:
Thus, the selling price is increased by 33%.

Find a percent of a whole:

1. 1% of 25
2. 18.2% of 50
3. of 100
4. 125% of 60

Find what percent one number is of another number.

1. 10 is what percent of 20?
2. 4 is what percent of 12?
3. 12 is what percent of 4?

Find the whole when the percent of it is given.

1. 15% of what number is 15?
2. of what number is 3?
3. 200% of what number is 20?

Now try your percent skills on some real-life problems.

1. The deputy chief, after reviewing the roll call, finds that 15% of the 115 members of B shift are absent due to illness and approved vacation. How many personnel have to be called in to fill in for the absent personnel?
2. a. 15       b. 17       c. 115       d. 132

3. Twenty percent of Engine 5's firefighters are women. If there are 30 women on the roster, how many total members are there?
4. a. 36       b. 70       c. 100       d. 150

5. During June, Firefighter Hanson's company responded to 150 alarms. Of these, 26 were wildland responses. What percent of the total alarms were wildland responses?
6. a. 12%       b. 17%       c. 22%       d. 26%

7. Chief Smith has approved a purchase of new turnout gloves at \$25.50 a pair. If his company received a government discount of 15%, what was the original price per pair?
8. a. \$25.50       b. \$27.50       c. \$28.45       d. \$30.00