# Markup and Markdown Problems

These lessons help Grade 7 students learn how to identify the original price as the whole and use their knowledge of percent and proportional relationships to solve multi-step markup and markdown problems.

### Lesson 7 Student Outcomes

• Students understand the terms original price, selling price, markup, markdown, markup rate, and markdown rate.
• Students identify the original price as the whole and use their knowledge of percent and proportional relationships to solve multistep markup and markdown problems.
• Students understand equations for markup and markdown problems and use them to solve markup and markdown problems.

Lesson 7 Classwork

Definitions:

• A markup is the amount of increase in a price.
• A markdown is the amount of decrease in a price.
• The original price is the starting price. It is sometimes called the cost or wholesale price.
• The selling price is the original price plus the markup or minus the markdown.
• The markup rate is the percent increase in the price, and the markdown rate (discount rate) is the percent decrease in the price.
• Most markup problems can be solved by the equation: (Selling Price) = (1 + m)(Whole), where m is the markup rate, and the whole is the original price.
• Most markdown problems can be solved by the equation: Selling Price) = (1 - m)(Whole), where m is the markdown rate, and the whole is the original price.

Example 1:
Games Galore Super Store buys the latest video game at a wholesale price of \$30.00. The markup rate at Game’s Galore Super Store is 40%. You use your allowance to purchase the game at the store. How much will you pay, not including tax?
a. Write an equation to find the price of the game at Games Galore Super Store. Explain your equation.
b. Solve the equation from part (a).
c. What was the total markup of the video game? Explain.
d. You and a friend are discussing markup rate. He says that an easier way to find the total markup is by multiplying the wholesale price of \$30 by 40%. Do you agree with him? Why or why not?

Example 2: Black Friday
A mountain bike is discounted by 30% and then discounted an additional 10% for shoppers who arrive before 5:00 a.m.
a. Find the sales price of the bicycle.
b. In all, by how much has the bicycle been discounted in dollars? Explain.
c. After both discounts were taken, what was the total percent discount?
d. Instead of purchasing the bike for \$300, how much would you save if you bought it before 5:00 a.m.?

Example 3: Working Backwards
A car that normally sells for \$20,000 is on sale for \$16,000. The sales tax is 7.5%.
a. What percent of the original price of the car is the final price?
b. Find the discount rate.
c. By law, sales tax has to be applied to the discount price. However, would it be better for the consumer if the 7.5% sales tax were calculated before the discount was applied? Why or why not?
d. Write an equation applying the commutative property to support your answer to part (c).

Exercises 1–3

1. Sasha went shopping and decided to purchase a set of bracelets for 25% off of the regular price. If Sasha buys the bracelets today, she will receive an additional 5%. Find the sales price of the set of bracelets with both discounts. How much money will Sasha save if she buys the bracelets today?
2. A golf store purchases a set of clubs at a wholesale price of \$250. Mr. Edmond learned that the clubs were marked up 200%. Is it possible to have a percent increase greater than 100%? What is the retail price of the clubs?
3. Is a percent increase of a set of golf clubs from \$250 to \$750 the same as a markup rate of 200%? Explain.

Exercise 4
a. Write an equation to determine the selling price, p, on an item that is originally priced s dollars after a markup of 25%.
b. Create a table (and label it) showing five possible pairs of solutions to the equation.
c. Create a graph (and label it) of the equation.
d. Interpret the points (0, 0) and (1, r).

Exercise 5
Use the following table to calculate the markup or markdown rate. Show your work. Is the relationship between the original price and selling price proportional or not? Explain.

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