GM Lesson 015 Percentage Profit and Loss

Learning Intentions

By the end of this lesson, students will be able to:

• Calculate profit and loss from cost price and selling price.
• Express profit or loss as a percentage of the cost price.
• Interpret percentage profit and loss in business contexts.

Prerequisites

Students should already be able to:

• Calculate percentage increase and percentage decrease.
• Calculate final prices after mark-ups and discounts.
• Identify the difference between an original value and a new value.
• Use a calculator to evaluate percentage expressions.
• Interpret money values in dollars and cents.

Key Idea Summary

A business makes a profit when the selling price is greater than the cost price.

A business makes a loss when the selling price is less than the cost price.

Profit or loss is usually expressed as a percentage of the cost price, because the cost price is the original amount paid by the business.

A positive result represents profit.

A negative result, or a stated loss, represents loss.

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

Introduction: Cost Price and Selling Price

Time: minutes

The cost price is the amount paid to buy or produce an item.

The selling price is the amount received when the item is sold.

If:

then there is a profit.

If:

then there is a loss.

If:

then there is neither profit nor loss. This is called breaking even.

Worked Example 1: Calculating Profit

A shop buys a pair of shoes for $ and sells them for $ .

Calculate the profit.

The profit is $ .

Worked Example 2: Calculating Percentage Profit

A bike store buys a helmet for $ and sells it for $ .

Calculate the percentage profit.

First calculate the profit.

Now express the profit as a percentage of the cost price.

The percentage profit is .

Worked Example 3: Calculating Loss

A second-hand phone is bought for $ and sold for $ .

Calculate the loss.

The loss is $ .

Worked Example 4: Calculating Percentage Loss

A market stall buys fruit for $ but only sells it for $ .

Calculate the percentage loss.

First calculate the loss.

Now express the loss as a percentage of the cost price.

The percentage loss is .

Worked Example 5: Interpreting Profit and Loss in Context

A small business buys a coffee machine for $ and later sells it for $ .

Determine whether the business made a profit or loss, then calculate the percentage profit or loss.

Since:

the business made a loss.

The business made a loss of $ , which is a loss.

Understanding Checks

Check 1

A retailer buys a jacket for $ and sells it for $ .

1. Is this a profit or a loss?
2. What is the dollar amount of the profit or loss?
3. What is the percentage profit or loss?

Check 2

A laptop is bought for $ and sold for $ .

1. Is this a profit or a loss?
2. What is the dollar amount of the profit or loss?
3. What is the percentage profit or loss?

Check 3

Explain why percentage profit and percentage loss are calculated using the cost price as the denominator rather than the selling price.

Check 4

A business says it made a profit of on an item that cost $ .

Without calculating the final selling price exactly, should the selling price be greater than, less than or equal to $ ? Explain.

Exercises

Simple Familiar Exercises

Exercise 1

A toy is bought for $ and sold for $ .

Calculate the profit.

Exercise 2

A book is bought for $ and sold for $ .

Calculate the loss.

Exercise 3

A shirt is bought for $ and sold for $ .

Calculate the percentage profit.

Exercise 4

A bag is bought for $ and sold for $ .

Calculate the percentage loss.

Exercise 5

Complete the table.

Item	Cost Price	Selling Price	Profit or Loss	Percentage difference
Watch	$	$		+25%
Chair	$	$
Headphones	$	$
Jacket	$	$

Complex Familiar Exercises

Exercise 6

A store buys a speaker for $ and sells it for $ .

Calculate:

1. the profit
2. the percentage profit

Exercise 7

A bicycle is bought for $ and sold for $ .

Calculate:

1. the loss
2. the percentage loss

Exercise 8

A café buys ingredients for $ and sells the finished cakes for $ .

Calculate the percentage profit.

Exercise 9

A furniture shop buys a table for $ and sells it at a loss of $ .

Calculate:

1. the selling price
2. the percentage loss

Exercise 10

A retailer buys a phone case for $ and wants to make a profit of .

Calculate:

1. the required profit
2. the required selling price

Homework Problems

Homework should take no more than minutes.

Problem 1

A pair of sunglasses is bought for $ and sold for $ .

Calculate the profit and the percentage profit.

Problem 2

A gaming controller is bought for $ and sold for $ .

Calculate the loss and the percentage loss.

Problem 3

A business buys a product for $ and wants to make a profit.

Calculate the required selling price.

Problem 4

A second-hand store buys a fridge for $ and sells it at a loss.

Calculate the selling price.

Problem 5

A shop buys notebooks for $ each and sells them for $ each.

Calculate:

1. the total cost price
2. the total selling price
3. the total profit
4. the percentage profit

Problem 6

A product is bought for $ and sold for $ .

A student says:

“The loss is only $ , so the percentage loss must be .”

Explain the error and calculate the correct percentage loss.

Next: GM Lesson 016 Goods and Services Tax