GM Lesson 014 Mark-ups and Discounts
Learning Intentions
By the end of the lesson, students will be able to:
- Calculate percentage mark-ups on original prices.
- Calculate percentage discounts from marked prices.
- Determine final prices after mark-ups or discounts.
Prerequisites
Students should already be able to:
- Calculate a percentage of a quantity.
- Apply percentage increase and percentage decrease.
- Convert percentages to decimal multipliers.
- Interpret money calculations in consumer contexts.
Key Idea Summary
A mark-up is an increase added to the original price or cost price of an item.
A discount is a decrease taken from a marked price or original selling price.
For a mark-up:
For a discount:
The multiplier method can be faster.
A
A
Direct Instruction and Worked Examples
Time Allocation
Time Allocation
Time Allocation
Link to original
- Introduction, warmup and vocabulary: 5 minutes
- Direct instruction: 15 minutes
- Understanding checks: 5 minutes
- Exercises: 20 minutes
- Homework: 20 to 30 minutes outside the lesson it was taught in.
Direct Instruction
Businesses often buy items at a cost price and then sell them for a higher price. The increase is called a mark-up.
For example, if a store buys an item for $
Customers often buy items during sales. A reduction from the marked price is called a discount.
For example, if an item is marked at $
A useful distinction is:
- A mark-up increases the price.
- A discount decreases the price.
- The percentage is always applied to the price stated in the question.
Worked Example 1: Calculating a Mark-up
A store buys a backpack for $
First calculate the mark-up amount:
So the mark-up is $
Now add the mark-up to the original price:
Therefore, the selling price is $
Worked Example 2: Using a Multiplier for Mark-up
A bicycle helmet costs a shop $
A
Convert
Calculate the selling price:
Therefore, the selling price is $
Worked Example 3: Calculating a Discount
A jacket is marked at $
First calculate the discount amount:
So the discount is $
Now subtract the discount from the marked price:
Therefore, the sale price is $
Worked Example 4: Using a Multiplier for Discount
A pair of shoes is marked at $
A
Convert
Calculate the sale price:
Therefore, the sale price is $
Worked Example 5: Mark-up Followed by Discount
A speaker costs a retailer $
First apply the
The marked price is $
Now apply the
Therefore, the final sale price is $
A
Understanding Checks
Check 1
A shirt costs a store $
a. What is the mark-up amount?
b. What is the selling price?
Check 2
A pair of jeans is marked at $
a. What is the discount amount?
b. What is the sale price?
Check 3
A phone case costs $
Which multiplier should be used?
A.
B.
C.
D.
Check 4
A book is marked at $
Which calculation gives the sale price?
A.
B.
C.
D.
Check 5
A student says:
A
mark-up followed by a discount returns an item to its original price.
Use an example with an original price of $
Exercises
Simple Familiar Exercises
Exercise 1
A water bottle costs a shop $
Find:
a. the mark-up amount
b. the selling price
Exercise 2
A hat is marked at $
Find:
a. the discount amount
b. the sale price
Exercise 3
A calculator costs $
Find the selling price.
Exercise 4
A pair of headphones is marked at $
Find the sale price.
Exercise 5
Complete the table.
| Original Price | Mark-up | Selling Price |
|---|---|---|
| $ | ||
| $ | ||
| $ | ||
| $ |
Exercise 6
Complete the table.
| Marked Price | Discount | Sale Price |
|---|---|---|
| $ | ||
| $ | ||
| $ | ||
| $ |
Complex Familiar Exercises
Exercise 7
A store buys a desk lamp for $
Find the selling price.
Exercise 8
A jacket is marked at $
Find the sale price.
Exercise 9
A retailer buys a pair of shoes for $
Later, the shoes are discounted by
Find the final sale price.
Exercise 10
A gaming keyboard is marked at $
Another store sells the same keyboard for $
Which store has the cheaper price, and by how much?
Exercise 11
A shop buys a watch for $
Find the percentage mark-up.
Use:
Exercise 12
A suitcase is marked at $
Find the percentage discount.
Use:
Homework Problems
Homework 1
A backpack costs a store $
Find the selling price.
Homework 2
A dress is marked at $
Find the sale price.
Homework 3
A laptop bag costs $
Later, it is discounted by
Find the final sale price.
Homework 4
A set of headphones is marked at $
Store A discounts the headphones by
Store B sells the same headphones for $
Which store has the cheaper price, and by how much?
Homework 5
A shop buys a jacket for $
Find the percentage mark-up.
Homework 6
A tablet is sold for $
Find the marked price before the discount.
Homework 7
A camping store buys sleeping bags for $
During a sale, the sleeping bags are discounted by
Find the final sale price.
Homework 8
A camera is marked at $
It is discounted by
Find the final sale price.