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# Applications of Percents in Word Problems Study Guide

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Updated on Oct 4, 2011

## Introduction to Applications of Percents in Word Problems

The longer mathematics lives the more abstract—and therefore, possibly also the more practical—it becomes.

—ERIC TEMPLE BELL (1883–1960)

This lesson takes the basics of percent and applies them to everyday problems. You will review important topics such as commission, tax, tip, discounts, and simple interest, as well as learn how to solve these practical applications of percent.

### Applications of Percent Word Problems

Most percent word problems can be solved using the proportion . This important proportion will be adjusted for each of the problem types that follow.

## Commission

Commission is the amount of money earned by a salesperson for selling a certain product. These products could be in the form of televisions, appliances, real estate (homes and property), and automobiles, to name a few. It is common for a salesperson's commission to be a percent of his or her total sales. To find the commission earned, use the proportion .

#### Example

Charles works at a job selling computer equipment. He receives 4% commission on his total sales for the month. What is the commission he earns if his monthly sales total is \$14,560?

To find the commission, use the proportion . Substitute the values, and the proportion becomes . Cross multiply to get 100x = 58,240. Divide each side of the equation to get

x = \$582.40

Charles makes \$582.40 in commission.

## Sales Tax

Sales tax is an amount of money added to a total purchase. This amount is usually a percent of the total sales, and is determined by the county and state in which the purchase is made. Use the proportion to solve sales tax problems.

#### Example

Toby buys a new MP3 player for a price of \$45.50. What is the total amount his credit card is charged if the sales tax is 7%?

To find the sales tax, use the proportion . Substitute the values, and the proportion becomes . Cross multiply to get 100x = 318.5. Divide each side of the equation to get

x = 3.185

which rounds to \$3.19. Toby pays \$3.19 in tax. Thus, the total amount that will be charged is \$45.50 + \$3.19 = \$48.69.

## Discount

A discount is an amount subtracted from the price of an item; it is the money you save when buying something. If a discount is a given dollar amount, just subtract this amount from the price of the item. For example, if a shirt is \$5.00 off the original price of \$20.00, the new price is \$20.00 – \$5.00 = \$15.00.

However, in other cases, the discount is given as a percent off the total amount purchased. Use the proportion to find the amount of discount, and then subtract from the original cost to find the sale price.

#### Example

Tara is shopping for a new jacket. The original price is \$55.00 with a discount of 30% off. What is the sale price of the jacket?

To find the sale price, first find the amount of discount. Use the proportion . Substitute into the proportion and get. Cross multiply to get 100x = 1,650. Divide each side of the equation by 100 to get

x = \$16.50

Tara will save \$16.50. Thus, the total sale price will be \$55 – \$16.50 = \$38.50.

#### Tip:

Tip, also known as gratuity, is the extra amount of money given to a person providing a service. This could be a server at a restaurant, a hairdresser, or a pet groomer, to name a few examples. Tip can be calculated by using the proportion .

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