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Homer received $1,140 commission when he sold a car for $28,500 . What rate of commission did he get?

4%

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Bernice earned $451 commission when she sold an $8,200 living room set. What rate of commission did she get?

5.5%

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Solve discount applications

Applications of discount are very common in retail settings [link] . When you buy an item on sale, the original price of the item has been reduced by some dollar amount. The discount rate , usually given as a percent, is used to determine the amount of the discount. To determine the amount of discount , we multiply the discount rate by the original price. We summarize the discount model in the box below.

The figure shows a sale sign with a discount rate
Applications of discounts are common in everyday life. (credit: Charleston's TheDigitel, Flickr)

Discount

An amount of discount is a percent off the original price.

amount of discount = discount rate · original price sale price = original price discount

The sale price should always be less than the original price. In some cases, the amount of discount is a fixed dollar amount. Then we just find the sale price by subtracting the amount of discount from the original price.

Jason bought a pair of sunglasses that were on sale for $10 off. The original price of the sunglasses was $39 . What was the sale price of the sunglasses?

Solution

Identify what you are asked to find. What is the sale price?
Choose a variable to represent it. Let s = the sale price.
Write a sentence that gives the information to find it. The sale price is the original price minus the discount.
Translate into an equation. .
Simplify. .
Write a complete sentence that answers the question. The sale price of the sunglasses was $29.
Check if this answer is reasonable. Yes. The sale price, $29, is less than the original price, $39.
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Marta bought a dishwasher that was on sale for $75 off. The original price of the dishwasher was $525 . What was the sale price of the dishwasher?

$450

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Orlando bought a pair of shoes that was on sale for $30 off. The original price of the shoes was $112 . What was the sale price of the shoes?

$82

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In [link] , the amount of discount was a set amount, $10 . In [link] the discount is given as a percent of the original price.

Elise bought a dress that was discounted 35% off of the original price of $140 . What was ⓐ the amount of discount and ⓑ the sale price of the dress?

Solution

Before beginning, you may find it helpful to organize the information in a list.
Original price = $140
Discount rate = 35%
Amount of discount = ?

Identify what you are asked to find. What is the amount of discount?
Choose a variable to represent it. Let d = the amount of discount.
Write a sentence that gives the information to find it. The discount is 35% of the original price.
Translate into an equation. .
Simplify. .
Write a complete sentence that answers the question. The amount of discount was $49.
Check if this answer is reasonable. Yes. A $49 discount is reasonable for a $140 dress.


Original price = $140
Amount of discount = $49
Sale price = ?

Identify what you are asked to find. What is the sale price of the dress?
Choose a variable to represent it. Let s = the sale price.
Write a sentence that gives the information to find it. The sale price is the original price minus the discount.
Translate into an equation. .
Simplify. .
Write a complete sentence that answers the question. The sale price of the dress was $91.
Check if this answer is reasonable. Yes. The sale price, $91, is less than the original price, $140.
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Practice Key Terms 9

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Source:  OpenStax, Prealgebra. OpenStax CNX. Jul 15, 2016 Download for free at http://legacy.cnx.org/content/col11756/1.9
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