## Discount Problems

### Learning outcome

• Use mathematical notation to solve discount problems Feminine Furnishings Bedding Sale

A store called Feminine Furnishings is having a sale on bedding. Their queen sheet sets have a list price of $126$. During the first two weeks of February, the store has a—Snuggle Up In Love Sale— where customers save $14\%$ on any white, pink, or red bedding set. Carly selects a bedding set with pink stripes and pays $108.36$.

Applications of discount are very common in retail settings. When you buy an item on sale, the original or list 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.

### Discount

An amount of discount is subtracted from the original price.

amount of discount = discount rate $\cdot$ 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. For example, as you walk into a store you may see a sign that says “Spend $100$ or more, and receive a $20$ discount!”

### example

Jason bought a pair of sunglasses from a rack that was labeled $\text{\10}$ off all Retrop brand glasses. The original price of the sunglasses was $\text{\39}$. What was the sale price of the sunglasses?

### try it

In the first example, the amount of discount was a set or static amount. In the next example, the discount is given as a percent of the original price.

### Example

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

### try it

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

### example

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.

### try it

In the following video we show another example of how to find the discount rate (also called the percent of change) given the original price and the marked-down price.

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