Learn on PengiBig Ideas Math, Course 2Chapter 6: Percents

Lesson 6: Discounts and Markups

In this Grade 7 lesson from Big Ideas Math, Course 2, Chapter 6, students learn how to calculate discounts and markups using percent of a number to find sale prices, original prices, and selling prices. Students apply two methods — subtracting the discount amount from the original price and multiplying by the remaining percent — as well as working backward from a sale price to find the original price using the percent proportion. Real-world contexts like retail pricing help students connect the concepts of discount and markup to everyday consumer math.

Section 1

Discount

Property

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

amount of discount=discount rateoriginal price\text{amount of discount} = \text{discount rate} \cdot \text{original price}
sale price=original priceamount of discount\text{sale price} = \text{original price} - \text{amount of discount}

Section 2

Finding Original Price from Sale Price

Property

When given a sale price and discount percentage, the original price can be found using:

original price=sale priceremaining percentage as decimal\text{original price} = \frac{\text{sale price}}{\text{remaining percentage as decimal}}

Where remaining percentage = 100%discount percentage100\% - \text{discount percentage}

Section 3

Mark-up

Property

The mark-up is the amount added to the wholesale price.

amount of mark-up=mark-up ratewholesale price\text{amount of mark-up} = \text{mark-up rate} \cdot \text{wholesale price}
list price=wholesale price+mark-up\text{list price} = \text{wholesale price} + \text{mark-up}

Lesson overview

Expand to review the lesson summary and core properties.

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Section 1

Discount

Property

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

amount of discount=discount rateoriginal price\text{amount of discount} = \text{discount rate} \cdot \text{original price}
sale price=original priceamount of discount\text{sale price} = \text{original price} - \text{amount of discount}

Section 2

Finding Original Price from Sale Price

Property

When given a sale price and discount percentage, the original price can be found using:

original price=sale priceremaining percentage as decimal\text{original price} = \frac{\text{sale price}}{\text{remaining percentage as decimal}}

Where remaining percentage = 100%discount percentage100\% - \text{discount percentage}

Section 3

Mark-up

Property

The mark-up is the amount added to the wholesale price.

amount of mark-up=mark-up ratewholesale price\text{amount of mark-up} = \text{mark-up rate} \cdot \text{wholesale price}
list price=wholesale price+mark-up\text{list price} = \text{wholesale price} + \text{mark-up}