Teacher Guide: Markup and Markdown

Learn how stores set prices with a markup on the cost price and lower them with a markdown, and how to find the percent, the original price and the result of stacked discounts.

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Learning Objectives

Calculate a selling price from a cost price and a markup percent
Calculate a sale price from an original price and a markdown percent
Find the percent of markup or markdown from two prices, using the correct base
Find the original price when the sale price and the discount are known
Explain why successive discounts, or a markup followed by a markdown, do not simply add up

Prerequisites

• Finding Percent of a Number
• Percent Increase and Decrease (multipliers 1 + p and 1 - d)
• Multiplying and dividing decimals

Discussion Starters

1. A shop advertises 20% off plus an extra 10% off. Is that the same as 30% off? How would you convince a friend?
2. Why do stores add a markup at all? What costs does it have to cover?
3. An item is marked up 25% and then marked down 25%. Is the store back where it started?
4. A tag shows only the sale price and 30% off. How can you find the original price?
5. Would you rather get 15% off and then 15% off again, or 30% off once? Why?

Common Misconceptions

Successive discounts can be added (20% + 10% = 30%)

Remediation: Use a concrete price of 100: after 20% off it is 80, and 10% of 80 is only 8, so the price is 72. The bar chart of 200, 160, 144 and 140 shows the gap.

The original price is the sale price plus the discount percent of the sale price

Remediation: Let students test their answer: 63 + 30% of 63 = 81.90, but 30% off 81.90 is 57.33, not 63. Then show the equation Original × 0.70 = 63.

A markdown of the same percent cancels a markup

Remediation: Draw two tape diagrams with different lengths: 25% of the longer selling price is a bigger piece than 25% of the cost price.

Differentiation Ideas

For Struggling Students:

• Start with prices of 100 so that the percent and the amount are the same number
• Use tape diagrams with 10 equal boxes to show 10% steps
• Practise markups and markdowns separately before mixing them

For On-Level Students:

• Find the percent of markup or markdown from two prices
• Work backwards from a sale price to the original price
• Compare two successive discounts with one single discount

For Advanced Students:

• Find the markdown that exactly undoes a given markup (25% up needs 20% down)
• Compare markup on cost with profit margin on the selling price
• Find the single discount equal to three stacked discounts

Standards Alignment

7.RP.A.3 (CCSS.MATH.CONTENT.7.RP.A.3)
Use proportional relationships to solve multistep ratio and percent problems, such as markups and markdowns, discounts, tax and commissions
7.EE.B.3 (CCSS.MATH.CONTENT.7.EE.B.3)
Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form

Lesson Resources

visualTape Diagrams for Cost, Markup and Discount
Shows the cost price as 100% with the markup added, and the original price as 100% with the discount taken off
activityPricing a Class Shop
Groups buy items at a cost price, choose a markup, then plan an end-of-season sale and check that they still make a profit
worksheetWhich Deal Is Better?
Compare stacked coupons with single discounts and find the real total discount

Lesson Content

Everything students see: definition, examples, common mistakes, applications. Tap to open.

Definition

A store buys an item at its cost price and sells it at a higher selling price. The extra amount is the markup. Later the store may lower the price: that reduction is a markdown (also called a discount), and the new price is the sale price.

Both use a multiplier:

\text{Selling price} = \text{Cost} \times (1 + p)

\text{Sale price} = \text{Original price} \times (1 - d)

Here

p

is the markup rate and

d

is the discount rate, written as decimals (25% =

0.25

Which price is the base?

A markup percent is always a percent of the cost price.
A markdown percent is always a percent of the original price (the price before the sale).

Two changes in a row multiply: 20% off and then 10% off gives

0.80 \times 0.90 = 0.72

, so you pay 72% and save 28%, not 30%.

Worked Examples

A sports shop buys a backpack for 40 dollars and adds a 35% markup. What is the selling price?

Find the markup amount (a percent of the cost)

$40 \times 0.35 = 14$ dollars → Markup = 14 dollars

Add it to the cost price

$40 + 14 = 54$ dollars

Check with the multiplier

$40 \times 1.35 = 54$ → Same answer

Answer: The backpack sells for 54 dollars.

Common Mistakes

Adding two discounts: 20% off and then 10% off = 30% off

Why it's wrong: The second discount is taken from the already reduced price, which is smaller than the original price, so it saves less.

Correct: Multiply the multipliers: $0.80 \times 0.90 = 0.72$ . You pay 72%, so the total discount is 28%.

Finding the original price by adding the percent to the sale price ( $63 + 30\%$ of $63 = 81.90$ )

Why it's wrong: The 30% was a percent of the original price, not of the sale price. Using the sale price as the base gives a number that is too small.

Correct: Divide by the multiplier: $63 \div 0.70 = 90$ . Check: $90 \times 0.70 = 63$ .

Dividing the markup by the selling price ( $\frac{90}{340} \approx 26\%$ )

Why it's wrong: A markup percent is measured against the cost price, the price the store paid.

Correct: Markup percent $= \frac{\text{markup}}{\text{cost}} \times 100\%$ , here $\frac{90}{250} = 36\%$ .

Thinking a 25% markdown undoes a 25% markup

Why it's wrong: The markdown is taken from the larger selling price, so it removes more than the markup added: $80 \times 1.25 = 100$ , then $100 \times 0.75 = 75$ .

Correct: The price ends 5 below the cost of 80. To get back from 100 to 80 you need a 20% markdown: $100 \times 0.80 = 80$ .

Why It Matters

In the lesson Percent Increase and Decrease you learned the multipliers

1 + p

and

1 - d

. Markup and markdown are where those multipliers meet real money:

Shops add a markup to cover rent, staff and profit before an item reaches the shelf.
Sales like 40% off are markdowns from the original price.
Stacked coupons (an extra 15% off at the checkout) are successive discounts, and they always save less than the two percents added together.
Price tags often show only the sale price, so finding the original price is a useful check.
Small businesses need to know whether a sale price is still above the cost price.

With these skills you can check any price tag and see which deal really is better.

Real World Applications

Clothing Store Pricing

Fashion shops often mark up new items a lot and mark them down at the end of the season. The question is whether the sale price still covers the cost.

Example:

A shirt bought for 20 dollars with a 100% markup sells for $20 \times 2 = 40$ dollars. Half price later is 20 dollars: no profit at all.

1Try It Yourself

A store buys a dress for 60 dollars and marks it up 50%. At the end of the season the dress is marked down 30%.

What is the final sale price in dollars?

Step 1: Write the mathematical expression

Apply the markup, then the markdown:

Stacked Coupons on Sale Days

On big sale days shops often offer a discount plus an extra coupon at the checkout. The coupon is taken from the already reduced price.

Example:

50% off and then an extra 50% off is not free: $0.5 \times 0.5 = 0.25$ , so you still pay 25% of the price.

2Try It Yourself

A TV costs 500 dollars. It is 20% off, and a coupon takes an extra 15% off the reduced price.

What is the total discount in percent? (Enter the number only.)

Step 1: Write the mathematical expression

Compare the final price with the original price:

Reading a Sale Tag

Outlet stores often show only the sale price and the discount. Working backwards tells you the original price and how much you really save.

Example:

A tag says 25% off, now 30 dollars. The original price was $30 \div 0.75 = 40$ dollars.

3Try It Yourself

A pair of sneakers has a tag: 40% off, now 48 dollars.

What was the original price in dollars?

Step 1: Write the mathematical expression

Divide the sale price by the multiplier:

Key Takeaways

1Selling price = cost price × (1 + markup rate); the markup percent is a percent of the cost price
2Sale price = original price × (1 - discount rate); the markdown percent is a percent of the original price
3Percent of markup = markup ÷ cost × 100%; percent of markdown = discount ÷ original price × 100%
4To find the original price from a sale price, divide by the multiplier (63 ÷ 0.70 = 90), never add the percent back
5Successive discounts multiply: 20% then 10% off is 0.80 × 0.90 = 0.72, a 28% discount, not 30%
6A markup followed by a markdown of the same percent ends below the start: 1.25 × 0.75 = 0.9375

Frequently Asked Questions

Is markup the same as profit margin?

No. Markup is a percent of the cost price, margin is a percent of the selling price. An item bought for 80 and sold for 100 has a 25% markup (20 of 80) but a 20% margin (20 of 100).

Can a markup be more than 100%?

Yes. A 100% markup doubles the cost price, and a 200% markup makes the selling price three times the cost. Some shops use markups this large on cheap items.

Can a markdown be more than 100%?

No. A 100% markdown already makes the price 0. A store cannot take off more than the whole price.

Does the order of two discounts matter?

No. Multiplication can be done in any order:

0.80 \times 0.90 = 0.90 \times 0.80 = 0.72

. 20% then 10% off gives the same price as 10% then 20% off.

Glossary

Cost price: The price a store pays for an item
Selling price: The price a store asks from customers: cost price plus markup
Markup: The amount (or percent of the cost price) a store adds to the cost price
Markdown (discount): The amount (or percent of the original price) taken off a price
Sale price: The price after a markdown
Multiplier: The number you multiply by to apply a percent change, such as 1.35 for a 35% markup or 0.60 for 40% off

Formula Card

Selling price

\text{Selling price} = \text{Cost} \times (1 + p)

Apply a markup of rate p to the cost price

Sale price

\text{Sale price} = \text{Original} \times (1 - d)

Apply a markdown of rate d to the original price

Percent of markup

\frac{\text{Selling price} - \text{Cost}}{\text{Cost}} \times 100\%

The base is the cost price

Percent of markdown

\frac{\text{Original} - \text{Sale price}}{\text{Original}} \times 100\%

The base is the original price

Original price

\text{Original} = \frac{\text{Sale price}}{1 - d}

Work backwards from a sale price

Teacher Guide: Markup and Markdown

Use this lesson with your class

For Teachers

For Struggling Students:

For On-Level Students:

For Advanced Students:

Lesson Content

Definition

Worked Examples

Common Mistakes

Why It Matters

Real World Applications

Clothing Store Pricing

Stacked Coupons on Sale Days

Reading a Sale Tag

Key Takeaways

Frequently Asked Questions

Glossary

Formula Card

Selling price

Sale price

Percent of markup

Percent of markdown

Original price

More in This Topic

Introduction to Percentages

Finding Percent of a Number

Percent Increase and Decrease

Percent Proportion