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 mark-up means the customer pays:

A discount means the customer pays:

Direct Instruction and Worked Examples

Time Allocation

Time Allocation

Time Allocation

  • 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.
Link to original

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 $ and applies a mark-up, the final price is more than $ .

Customers often buy items during sales. A reduction from the marked price is called a discount.

For example, if an item is marked at $ and has a discount, the final price is less than $ .

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 $ and applies a mark-up. Find the selling price.

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 $ . The shop applies a mark-up. Find the selling price.

A mark-up means the final price is:

Convert to a decimal multiplier:

Calculate the selling price:

Therefore, the selling price is $ .

Worked Example 3: Calculating a Discount

A jacket is marked at $ . It is discounted by . Find the sale price.

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 $ and discounted by . Find the sale price.

A discount means the customer pays:

Convert to a decimal multiplier:

Calculate the sale price:

Therefore, the sale price is $ .

Worked Example 5: Mark-up Followed by Discount

A speaker costs a retailer $ . The retailer applies a mark-up. Later, the marked price is discounted by . Find the final sale price.

First apply the mark-up:

The marked price is $ .

Now apply the discount:

Therefore, the final sale price is $ .

A mark-up followed by a discount does not return the item to its original price, because the two percentages are applied to different amounts.

Understanding Checks

Check 1

A shirt costs a store $ . The store applies a mark-up.

a. What is the mark-up amount?

b. What is the selling price?

Check 2

A pair of jeans is marked at $ . It is discounted by .

a. What is the discount amount?

b. What is the sale price?

Check 3

A phone case costs $ wholesale. It is marked up by .

Which multiplier should be used?

A.

B.

C.

D.

Check 4

A book is marked at $ and discounted by .

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 $ to decide whether the student is correct. (Hint: it is not)

Exercises

Simple Familiar Exercises

Exercise 1

A water bottle costs a shop $ . The shop applies a mark-up.

Find:

a. the mark-up amount

b. the selling price

Exercise 2

A hat is marked at $ . It is discounted by .

Find:

a. the discount amount

b. the sale price

Exercise 3

A calculator costs $ wholesale. It is marked up by .

Find the selling price.

Exercise 4

A pair of headphones is marked at $ . It is discounted by .

Find the sale price.

Exercise 5

Complete the table.

Original PriceMark-upSelling Price
$
$
$
$

Exercise 6

Complete the table.

Marked PriceDiscountSale Price
$
$
$
$

Complex Familiar Exercises

Exercise 7

A store buys a desk lamp for $ and applies a mark-up.

Find the selling price.

Exercise 8

A jacket is marked at $ . During a sale, it is discounted by .

Find the sale price.

Exercise 9

A retailer buys a pair of shoes for $ and marks them up by .

Later, the shoes are discounted by .

Find the final sale price.

Exercise 10

A gaming keyboard is marked at $ . It is discounted by in one store.

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 $ and wants to sell it for $ .

Find the percentage mark-up.

Use:

Exercise 12

A suitcase is marked at $ . After a discount, it sells for $ .

Find the percentage discount.

Use:

Homework Problems

Homework 1

A backpack costs a store $ . The store applies a mark-up.

Find the selling price.

Homework 2

A dress is marked at $ . It is discounted by .

Find the sale price.

Homework 3

A laptop bag costs $ wholesale. It is marked up by .

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 $ and sells it for $ .

Find the percentage mark-up.

Homework 6

A tablet is sold for $ after a discount.

Find the marked price before the discount.

Homework 7

A camping store buys sleeping bags for $ each and marks them up by .

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 , then discounted by a further .

Find the final sale price.

Next: GM Lesson 015 Percentage Profit and Loss