Learn on PengiReveal Math, AcceleratedUnit 3: Solve Problems Involving Percentages

Lesson 3-4: Solve Markup and Markdown Problems

In this Grade 7 lesson from Reveal Math, Accelerated, students learn how to solve markup and markdown problems by applying the percent equation to calculate price increases above manufacturing cost and price reductions from an original selling price. Using tape diagrams and two solution strategies, students practice finding customer cost after a markup percentage and the discounted price after a markdown percentage. The lesson connects these concepts to real-world retail scenarios such as pricing jeans, bird feeders, and sunglasses.

Section 1

Application: Finding Markups and Discounts

Property

A markup results when a percent of increase is applied to a cost. A discount results when a percent of decrease is applied to a cost.
New Price = Original Price + Markup
New Price = Original Price - Discount

Examples

  • A store buys a keyboard for 50 dollars and marks it up by 80%. The markup is 0.80⋅50=400.80 \cdot 50 = 40 dollars. The new price is 50+40=9050 + 40 = 90 dollars.
  • A 30 dollars hoodie is on sale for 20% off. The discount is 0.20⋅30=60.20 \cdot 30 = 6 dollars. The new price is 30−6=2430 - 6 = 24 dollars.

Explanation

Stores use markups to make a profit—they buy an item cheap and sell it for more! For you, a discount is awesome because it means a sale! You calculate the percentage of the original price and either add it (markup) or subtract it (discount) to find the final price. This is the math behind every price tag.

Section 2

Multiplicative Shortcuts for Markups and Discounts

Property

You can calculate the final price of an item after a markup or discount in a single step by multiplying the original price by a factor based on the percent change. Let pp represent the percent markup or discount written as a decimal.

For a markup:

Section 3

Finding Original Prices Using Equations

Property

To find the original price when you know the final price after a discount or markup, set up an equation. Let a variable represent the unknown original price and solve for it.
For a discount:

Original Price×(1−discount decimal)=Sale Price\text{Original Price} \times (1 - \text{discount decimal}) = \text{Sale Price}
.
For a markup:
Original Price×(1+markup decimal)=Final Price\text{Original Price} \times (1 + \text{markup decimal}) = \text{Final Price}
.

Examples

  • A shirt is on sale for 36 dollars after a 25% discount. To find the original price pp, solve the equation p(1−0.25)=36p(1 - 0.25) = 36, or 0.75p=360.75p = 36. Dividing by 0.75 gives p=48p = 48 dollars.
  • A store sells a jacket for 180 dollars after marking it up 20% from wholesale. The wholesale price ww can be found with w(1+0.20)=180w(1 + 0.20) = 180, or 1.20w=1801.20w = 180. The wholesale price was w=150w = 150 dollars.
  • A video game costs 42 dollars after a 30% discount. To find the original price xx, solve x(1−0.30)=42x(1 - 0.30) = 42, or 0.70x=420.70x = 42. The original price was x=60x = 60 dollars.

Explanation

Sometimes you know the sale price after a discount or the final price after a markup, but need to find the original price. You can work backward using an equation. If a 25% discount resulted in a 75 dollars sale price, you know that 75% of the original price equals 75 dollars.

Lesson overview

Expand to review the lesson summary and core properties.

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Section 1

Application: Finding Markups and Discounts

Property

A markup results when a percent of increase is applied to a cost. A discount results when a percent of decrease is applied to a cost.
New Price = Original Price + Markup
New Price = Original Price - Discount

Examples

  • A store buys a keyboard for 50 dollars and marks it up by 80%. The markup is 0.80⋅50=400.80 \cdot 50 = 40 dollars. The new price is 50+40=9050 + 40 = 90 dollars.
  • A 30 dollars hoodie is on sale for 20% off. The discount is 0.20⋅30=60.20 \cdot 30 = 6 dollars. The new price is 30−6=2430 - 6 = 24 dollars.

Explanation

Stores use markups to make a profit—they buy an item cheap and sell it for more! For you, a discount is awesome because it means a sale! You calculate the percentage of the original price and either add it (markup) or subtract it (discount) to find the final price. This is the math behind every price tag.

Section 2

Multiplicative Shortcuts for Markups and Discounts

Property

You can calculate the final price of an item after a markup or discount in a single step by multiplying the original price by a factor based on the percent change. Let pp represent the percent markup or discount written as a decimal.

For a markup:

Section 3

Finding Original Prices Using Equations

Property

To find the original price when you know the final price after a discount or markup, set up an equation. Let a variable represent the unknown original price and solve for it.
For a discount:

Original Price×(1−discount decimal)=Sale Price\text{Original Price} \times (1 - \text{discount decimal}) = \text{Sale Price}
.
For a markup:
Original Price×(1+markup decimal)=Final Price\text{Original Price} \times (1 + \text{markup decimal}) = \text{Final Price}
.

Examples

  • A shirt is on sale for 36 dollars after a 25% discount. To find the original price pp, solve the equation p(1−0.25)=36p(1 - 0.25) = 36, or 0.75p=360.75p = 36. Dividing by 0.75 gives p=48p = 48 dollars.
  • A store sells a jacket for 180 dollars after marking it up 20% from wholesale. The wholesale price ww can be found with w(1+0.20)=180w(1 + 0.20) = 180, or 1.20w=1801.20w = 180. The wholesale price was w=150w = 150 dollars.
  • A video game costs 42 dollars after a 30% discount. To find the original price xx, solve x(1−0.30)=42x(1 - 0.30) = 42, or 0.70x=420.70x = 42. The original price was x=60x = 60 dollars.

Explanation

Sometimes you know the sale price after a discount or the final price after a markup, but need to find the original price. You can work backward using an equation. If a 25% discount resulted in a 75 dollars sale price, you know that 75% of the original price equals 75 dollars.