### Learning outcome

- Use mathematical notation to solve discount problems

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

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 [latex]\cdot[/latex] original price**

**sale price = original price [latex]-[/latex] 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 [latex]$100[/latex] or more, and receive a [latex]$20[/latex] discount!”

### example

Jason bought a pair of sunglasses from a rack that was labeled [latex]\text{\$10}[/latex] off all Retrop brand glasses. The original price of the sunglasses was [latex]\text{\$39}[/latex]. 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 [latex]\text{35%}[/latex] off of the original price of [latex]\text{\$140}[/latex]. 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 [latex]\text{\$13.95}[/latex]. The original price of the swimsuit was [latex]\text{\$31}[/latex]. 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.