Discounts and sale prices | Year 7

01 / LEARN

Understand the idea.

Two amounts, two meanings

A discount is the saving removed from the original price. Find that percentage of the original amount, then subtract the saving to find the sale price. Label the two amounts because they answer different questions.

A $20 %$ discount leaves $80 %$ to pay. The original price is the whole in both calculations. Keep exact amounts during the working and write money to two decimal places when cents need to be shown.

Use the percentage left

You can calculate the percentage left directly: after a discount of $d %$ , the customer pays $(100 - d) %$ of the original price. This is equivalent to finding the saving and subtracting it once.

Compare offers by the final cost for the same item or quantity. A larger discount can still leave a higher price when the starting prices differ. Add any stated compulsory delivery or booking charge to the discounted item price.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Find the saving, then subtract

A 75-dollar jacket is discounted by $20 %$ . Find the saving and sale price.

Worked solution

1
Find the discount share.
$20 % = \frac{20}{100} = \frac{1}{5}$
The saving is one fifth of the original price.
2
Calculate the saving.
$75 \div 5 = 15 dollars$
The discount applies to the original seventy-five-dollar price.
3
Subtract the saving.
$75 - 15 = 60 dollars$
The sale price is the original price with the discount removed.

Answer

Saving: 15 dollars; sale price: 60 dollars.

EXAMPLE 02

Compare two offers

Shop A sells a game for 40 dollars with $15 %$ off. Shop B sells the same game for 35 dollars. Which is cheaper?

Worked solution

1
Calculate Shop A's saving.
$\frac{15}{100} \times 40 = 6 dollars$
Fifteen percent is taken from Shop A’s original forty-dollar price.
2
Find Shop A's final price.
$40 - 6 = 34 dollars$
The saving must be subtracted before comparing the offers.
3
Compare the final prices.
$35 - 34 = 1 dollar$
Shop A costs thirty-four dollars and Shop B costs thirty-five dollars, so A is cheaper by one dollar.

Answer

Shop A, by 1 dollar.

03 / YOUR TURN

Try it yourself.

Check your understanding

An item costs 50 dollars before a $10 %$ discount. Find the price paid.

Show answer & reasoning

45 dollars

The saving is $\frac{10}{100} \times 50 = 5$ dollars. Subtract it from the original price to obtain $50 - 5 = 45$ dollars paid.

Keep practising

6 worksheet questions · 15 marks

Open worksheet Worked solutions

Read the questions online

Find the saving on a 60-dollar bag with $25 %$ off.
2 marks
Find the sale price of a 90-dollar item with $10 %$ off.
2 marks
A 48-dollar item is discounted by $50 %$ . Find its sale price.
2 marks
Find the sale price after $15 %$ off 80 dollars.
3 marks
Shop A charges 70 dollars with $20 %$ off. Shop B charges 60 dollars. Which is cheaper, and by how much?
3 marks
A 120-dollar bike has $25 %$ off, but delivery costs 12 dollars. What is the total cost?
3 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

Find the saving on a 60-dollar bag with $25 %$ off.
2 marks
One quarter of 60 is 15.
15 dollars
Find the sale price of a 90-dollar item with $10 %$ off.
2 marks
$Saving = 9$ dollars; $90 - 9 = 81$ .
81 dollars
A 48-dollar item is discounted by $50 %$ . Find its sale price.
2 marks
Half the original price remains.
24 dollars
Find the sale price after $15 %$ off 80 dollars.
3 marks
10 percent is 8 dollars and 5 percent is 4 dollars.
$Saving = 12$ dollars; $price paid = 80 - 12 = 68$ .
68 dollars
Shop A charges 70 dollars with $20 %$ off. Shop B charges 60 dollars. Which is cheaper, and by how much?
3 marks
A saves 14 dollars and costs 56 dollars.
$60 - 56 = 4$ dollars.
Shop A by 4 dollars.
A 120-dollar bike has $25 %$ off, but delivery costs 12 dollars. What is the total cost?
3 marks
$Saving = 30$ dollars, so $bike price = 90$ dollars.
Add delivery: $90 + 12 = 102$ dollars.
102 dollars

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Curriculum reference & lesson scope

Australian Curriculum v9 / SA Curriculum Mathematics

Fractions–decimals–percentages; percentages of quantities; expressing one amount as a percentage of another; discounts and sale prices; practical spending/budget comparisons; choosing and explaining a financial model.

Official curriculum source ↗

In this lesson

Understand the idea.

Two amounts, two meanings

Use the percentage left

See the method in action.

Find the saving, then subtract

Find the discount share.

Calculate the saving.

Subtract the saving.

Compare two offers

Calculate Shop A's saving.

Find Shop A's final price.

Compare the final prices.

Try it yourself.

Check your understanding

Keep practising