6.3 Solve sales tax, commission, and discount applications  (Page 4/15)

There may be times when you buy something on sale and want to know the discount rate. The next example will show this case.

Jeannette bought a swimsuit at a sale price of $\text{\$13.95}.$ The original price of the swimsuit was $\text{\$31}.$ Find the ⓐ amount of discount and ⓑ discount rate.

Solution

ⓐ Before beginning, you may find it helpful to organize the information in a list.
Original price = $31
Amount of discount = ?
Sale price = $13.95

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 the original price minus the sale price.
Translate into an equation.
Simplify.
Write a complete sentence that answers the question.	The amount of discount was $17.05.
Check if this answer is reasonable.	Yes. The $17.05 discount is less than the original price.

ⓑ Before beginning, you may find it helpful to organize the information in a list.
Original price = $31
Amount of discount = $17.05
Discount rate = ?

Identify what you are asked to find.	What is the discount rate?
Choose a variable to represent it.	Let $r=$ the discount rate.
Write a sentence that gives the information to find it.	The discount is what percent of the original price?
Translate into an equation.
Divide.
Simplify.
Write a complete sentence that answers the question.	The rate of discount was 55%.
Check if this answer is reasonable.	The rate of discount was a little more than 505 and the amount of discount is a little more than half of $31.

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Solve mark-up applications

Applications of mark-up are very common in retail settings. The price a retailer pays for an item is called the wholesale price . The retailer then adds a mark-up to the wholesale price to get the list price , the price he sells the item for. The mark-up is usually calculated as a percent of the wholesale price. The percent is called the mark-up rate . To determine the amount of mark-up, multiply the mark-up rate by the wholesale price. We summarize the mark-up model in the box below.

The list price should always be more than the wholesale price.

Adam's art gallery bought a photograph at the wholesale price of $\text{\$250}.$ Adam marked the price up $\text{40\%}.$ Find the ⓐ amount of mark-up and ⓑ the list price of the photograph.

Solution

ⓐ
Identify what you are asked to find.	What is the amount of mark-up?
Choose a variable to represent it.	Let $m=$ the amount of each mark-up.
Write a sentence that gives the information to find it.	The mark-up is 40% of the wholesale price.
Translate into an equation.
Simplify.
Write a complete sentence that answers the question.	The mark-up on the photograph was $100.
Check if this answer is reasonable.	Yes. The markup rate is less than 50% and $100 is less than half of $250.

ⓑ
Identify what you are asked to find.	What is the list price?
Choose a variable to represent it.	Let $p=$ the list price.
Write a sentence that gives the information to find it.	The list price is the wholesale price plus the mark-up.
Translate into an equation.
Simplify.
Write a complete sentence that answers the question.	The list price of the photograph was $350.
Check if this answer is reasonable.	Yes. The list price, $350, is more than the wholesale price, $250.

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