Introduction
Markups, Discounts, and Sales Tax is an important Grade 7 math skill because students are moving from simple answers toward explaining how the math works.
In this lesson, students use models, real questions, worked examples, practice problems, and two online quizzes to build confidence with markups, discounts, and sales tax.
What Is Markups, Discounts, and Sales Tax?
Markups, Discounts, and Sales Tax means choosing a model, naming what each number means, and explaining the strategy.
The goal is not only to get the answer. Students should be able to show the idea, explain the strategy, and check whether the answer makes sense.
Understanding Markups, Discounts, and Sales Tax
Before solving, students should slow down and decide what each number, shape, unit, or label represents.
- Read the question carefully and identify what is being asked.
- Choose a model, equation, table, or diagram that matches the situation.
- Solve one step at a time and keep units or labels attached.
- Use the answer explanation to check that the result makes sense.
Visual Models
Visual Model 1
Question: A book store displays a book with original price \($80\) and a discount tag showing \(22.5\%\) off. What is the sale price?
- A. \($57.50\)
- B. \($18\)
- C. \($61.00\)
- D. \($62\)
Why it works: Discount \(=0.225\times80=$18\). Sale price \(=80-18=$62\).
Answer: \($62\)
Visual Model 2
Question: A store uses a consistent markup strategy. Based on the table, what should be the selling price for an item that costs \($50\)?
- A. \($65\)
- B. \($75\)
- C. \($60\)
- D. \($70\)
Why it works: From row 1: markup is \(56-40=$16\) on cost of \($40\), a \(40\%\) markup. For cost \($50\): markup \(=0.40\times50=$20\), so selling price \(=50+20=$70\).
Answer: \($70\)
Worked Examples
Example 1
Question: A discount bar shows original price \($60\) and sale price \($36\). What percent discount was applied?
- A. \(30\%\)
- B. \(24\%\)
- C. \(36\%\)
- D. \(40\%\)
- Discount amount \(=60-36=$24\).
- Percent \(=(24/60)\times100=40\%\).
Answer: \(40\%\)
Example 2
Question: A store applies consistent discount rates. Based on the table, what is the discount percent for both items?
- A. \(10\%\)
- B. \(33\%\)
- C. \(25\%\)
- D. \(20\%\)
- Widget: discount \(=(20-16)/20=4/20=0.20=20\%\).
- Gadget: discount \(=(30-24)/30=6/30=0.20=20\%\).
- Both are \(20\%\) off.
Answer: \(20\%\)
Example 3
Question: A store offers a \(25\%\) discount on a shirt originally priced at \($32\). What is the sale price?
- A. \($8\)
- B. \($40\)
- C. \($28\)
- D. \($24\)
- Discount amount \(=0.25\times32=$8\).
- Sale price \(=32-8=$24\).
Answer: \($24\)
Real-World Word Problems
Problem 1
Question: A pair of shoes costs \($60\). If a store marks up the wholesale cost by \(50\%\), what is the selling price?
- A. \($110\)
- B. \($40\)
- C. \($30\)
- D. \($90\)
Why it works: Markup amount \(=0.50\times60=$30\). Selling price \(=60+30=$90\).
Answer: \($90\)
Problem 2
Question: A jacket has a sale price of \($45\) after a \(10\%\) discount. What was the original price?
- A. \($49.50\)
- B. \($54\)
- C. \($40.50\)
- D. \($50\)
Why it works: Sale price \(=\) original price \(\times(1-0.10)\). So \(45=\text{original}\times0.90\), giving original \(=45\div0.90=$50\).
Answer: \($50\)
Common Mistakes
- Rushing before identifying what the numbers represent.
- Choosing an operation that does not match the situation.
- Dropping labels, units, or context from the answer.
- Skipping the estimate or reasonableness check.
Strategy Tips
- Underline the question being asked.
- Use a model before jumping to computation.
- Write an equation that matches the story or picture.
- Explain the final answer in a sentence.
Practice Questions
Question 1
A retailer sells an item for \($110\) after marking up the cost by \(10\%\). What was the original cost?
- A. \($99\)
- B. \($95\)
- C. \($121\)
- D. \($100\)
Question 2
A toy costs \($20\) at a store. The store adds an \(8\%\) sales tax. What is the final price?
- A. \($20.80\)
- B. \($28\)
- C. \($22\)
- D. \($21.60\)
Question 3
A book is marked down by \(30\%\) from its original price of \($25\). What is the discount amount?
- A. \($22.50\)
- B. \($17.50\)
- C. \($15\)
- D. \($7.50\)
Question 4
A retailer buys backpacks for \($40\) each and marks them up by \(75\%\). What is the selling price?
- A. \($60\)
- B. \($105\)
- C. \($115\)
- D. \($70\)
Question 5
A video game originally costs \($50\). After a \(20\%\) discount, a customer buys it. If the sales tax is \(6\%\), what is the final amount paid?
- A. \($40.00\)
- B. \($47.00\)
- C. \($37.60\)
- D. \($42.40\)
Question 6
A dress is on sale for \($36\) after a \(40\%\) markdown. What was the original selling price?
- A. \($56.40\)
- B. \($86.40\)
- C. \($50\)
- D. \($60\)
Full Answer Explanations Click to show all answers and explanations
Question 1
Answer: \($100\)
Selling price \(=\) cost \(\times(1+0.10)\). So \(110=\text{cost}\times1.10\), giving cost \(=110\div1.10=$100\).
Question 2
Answer: \($21.60\)
Tax \(=0.08\times20=$1.60\). Final price \(=20+1.60=$21.60\).
Question 3
Answer: \($7.50\)
Discount amount \(=0.30\times25=$7.50\).
Question 4
Answer: \($70\)
Markup \(=0.75\times40=$30\). Selling price \(=40+30=$70\).
Question 5
Answer: \($42.40\)
After discount: \(50-0.20(50)=$40\). Tax on \($40\): \(0.06(40)=$2.40\). Final: \(40+2.40=$42.40\).
Question 6
Answer: \($60\)
Sale price \(=\) original \(\times0.60\). So \(36=\text{original}\times0.60\), giving original \(=36\div0.60=$60\).
Connection to Standards
This lesson supports Grade 7 math expectations for reasoning, modeling, problem solving, and explaining answers clearly. It connects classroom skills to the kind of questions students see on state math assessments.
Summary
Markups, Discounts, and Sales Tax becomes easier when students connect the question to a model, use clear steps, and explain why the answer fits.
GOLDEN RULE
Understand the model before choosing the operation.
