# 2.2: Discount Problems

- Page ID
- 45782

### 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 . During the first two weeks of February, the store has a—Snuggle Up In Love Sale— where customers save on any white, pink, or red bedding set. Carly selects a bedding set with pink stripes and pays .

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 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 or more, and receive a discount!”

### example

Jason bought a pair of sunglasses from a rack that was labeled off all Retrop brand glasses. The original price of the sunglasses was . What was the sale price of the sunglasses?

[reveal-answer q=”967734″]Show Answer[/reveal-answer]

[hidden-answer a=”967734″]

Solution

Identify what you are asked to find. | What is the sale price? |

Choose a variable to represent it. | Let 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. | |

Check if this answer is reasonable. | |

Yes. The sale price, , is less than the original price, . | |

Write a complete sentence that answers the question. | The sale price of the sunglasses was . |

[/hidden-answer]

### try it

[ohm_question]146772[/ohm_question]

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 off of the original price of . What was the amount of discount and the sale price of the dress?

[reveal-answer q=”967374″]Show Answer[/reveal-answer]

[hidden-answer a=”967374″]

Solution

ⓐ Before beginning, you may find it helpful to organize the information in a list.

Original price =

Discount rate =

Amount of discount = ?

Identify what you are asked to find. | What is the amount of discount? |

Choose a variable to represent it. | Let the amount of discount. |

Write a sentence that gives the information to find it. | The discount is of the original price. |

Translate into an equation. | |

Simplify. | |

Check if this answer is reasonable. | |

Yes. A discount is reasonable for a dress. | |

Write a complete sentence that answers the question. | The amount of discount was . |

ⓑ

Original price =

Amount of discount =

Sale price = ?

Identify what you are asked to find. | What is the sale price of the dress? |

Choose a variable to represent it. | Let 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. | |

Check if this answer is reasonable. | |

Yes. The sale price, , is less than the original price, . | |

Write a complete sentence that answers the question. | The sale price of the dress was . |

[/hidden-answer]

### try it

[ohm_question]146775[/ohm_question]

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 . The original price of the swimsuit was . Find the ⓐ amount of discount and ⓑ discount rate.

[reveal-answer q=”123339″]Show Answer[/reveal-answer]

[hidden-answer a=”123339″]

Solution

ⓐ Before beginning, you may find it helpful to organize the information in a list.

Original price =

Amount of discount = ?

Sale price =

Identify what you are asked to find. | What is the amount of discount? |

Choose a variable to represent it. | Let 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. | |

Check if this answer is reasonable. | |

Yes. The discount is less than the original price. | |

Write a complete sentence that answers the question. | The amount of discount was . |

ⓑ Before beginning, you may find it helpful to organize the information in a list.

Original price =

Amount of discount =

Discount rate = ?

Identify what you are asked to find. | What is the discount rate? |

Choose a variable to represent it. | Let 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. | |

Check if this answer is reasonable. | |

The rate of discount was a little more than and the amount of discount is a little more than half of . | |

Write a complete sentence that answers the question. | The rate of discount was . |

[/hidden-answer]

### try it

[ohm_question]156971[/ohm_question]

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.

- Screenshot from Big W Square Bedroom Video.
**Authored by**: Clay Fisher.**Located at**: https://vimeo.com/266614917.**License**:*CC BY: Attribution*

- Prealgebra.
**Provided by**: OpenStax.**License**:*CC BY: Attribution*.**License Terms**: Download for free at http://cnx.org/contents/caa57dab-41c...cda5519c@9.757