Discounts and sale prices | Year 7

01 / LEARN

The idea, step by step

Two amounts, two meanings

A discount is the amount removed from an original price. The sale price is the original price minus that saving. A 20 percent discount does not mean that you pay 20 percent of the original price.

Write both amounts with labels. This prevents a common mistake: finding the saving correctly but reporting it as the price paid. Round displayed money to cents only when needed.

Use the percentage left

After a 20 percent discount, 80 percent of the original price remains. Finding that remaining percentage is an alternative to calculating the saving and then subtracting.

Compare offers by their final cost for the same item or quantity. A larger discount percentage need not give the lower price if the original prices differ. Include any stated delivery fee after calculating the item discount.

A common trap

A 25 percent discount on an 80-dollar item means its sale price is 20 dollars.

Instead: 20 dollars is the saving. Subtract it from 80 dollars to obtain the 60-dollar sale price.

02 / WORKED EXAMPLES

See the thinking

Example 1

Find the saving, then subtract

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

$20 %$ of 75 is $\frac{1}{5} \times 75 = 15$ dollars.
Sale price = 75 - 15 = 60 dollars.

Saving: 15 dollars; sale price: 60 dollars.

Example 2

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?

$15 %$ of 40 is 6 dollars.
Shop A final price is 40 - 6 = 34 dollars.
Shop B costs 35 dollars, so A is 1 dollar cheaper.

Shop A, by 1 dollar.

Check your understanding

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

Show answer

45 dollars

Ten percent is 5 dollars; 50 - 5 = 45.

03 / WORKSHEET

Your turn

6 questions · 15 marks · Work at your own pace.

Worksheet PDF 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 ↗

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