Discounts and mark-ups | Year 8

01 / LEARN

Understand the idea.

Keep the price stages separate

Keep cost price, listed price and sale price separate. A mark-up on cost uses the cost as $100 %$ ; a later discount usually uses the listed price as $100 %$ . Label each stage so the percentage has the correct base.

Work through the price stages in order: add the mark-up to form the listed price, then apply the discount to find the actual selling price. Profit in dollars is selling price minus cost. A discounted item can still sell above its cost.

Compare profit and percentage language

A $25 %$ mark-up uses multiplier $1.25$ ; a $20 %$ discount uses multiplier $0.8$ . Multiply these stage multipliers to find the overall change. Subtracting the two percentage rates ignores that they act on different amounts.

To state profit as a percentage of cost, calculate $\frac{profit}{cost} \times 100 %$ . A percentage based on selling price would have a different denominator. Always read which price is the reference amount before forming the fraction.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Mark up a cost

A shop buys a lamp for 40 AUD and adds a 25% mark-up. Find the listed price.

Worked solution

1
Find the mark-up amount.
$40 \times 0.25 = 10 AUD$
Twenty-five percent is one quarter of the forty-dollar cost.
2
Add the mark-up to the cost.
$40 + 10 = 50 AUD$
The listed price includes the original cost and the additional ten dollars.
3
Check with a multiplier.
$40 \times 1.25 = 50 AUD$
One hundred and twenty-five percent includes the original whole and the mark-up.

Answer

50 AUD

EXAMPLE 02

A sale can still make a profit

An item costs a shop 50 AUD. It is marked up by 40%, then discounted by 20%. Find the sale price and profit.

Worked solution

1
Calculate the listed price.
$50 \times 1.4 = 70 AUD$
A forty percent mark-up makes the listed price one hundred and forty percent of cost.
2
Apply the discount to that price.
$70 \times 0.8 = 56 AUD$
The customer pays eighty percent of the seventy-dollar listed price.
3
Find the actual profit.
$56 - 50 = 6 AUD$
Profit compares the actual sale proceeds with the shop's original cost.
4
Express the profit relative to cost.
$\frac{6}{50} \times 100 % = 12 %$
The denominator is fifty because the requested profit percentage uses cost as its base.

Answer

Sale price 56 AUD; profit 6 AUD, or 12% of cost.

03 / YOUR TURN

Try it yourself.

Check your understanding

An item costing 60 AUD is marked up by 20%. Find the listed price.

Show answer & reasoning

72 AUD

The listed price retains the full cost plus $20 %$ : $60 \times 1.2 = 72 AUD$ . The mark-up itself is $12 AUD$ .

Keep practising

6 worksheet questions · 16 marks

Open worksheet Worked solutions

Read the questions online

Mark up a 30 AUD cost by 20%.
2 marks
Discount a listed price of 90 AUD by 10%.
2 marks
An item costs 48 AUD and is sold for 60 AUD. Find its dollar profit and percentage profit on cost.
3 marks
A listed price of 80 AUD is reduced by 15%. Find the sale price.
2 marks
An item costs 80 AUD. It is marked up by 25%, then discounted by 10%. Find its final price and profit on cost.
4 marks
A store buys a book for 24 AUD and lists it at 30 AUD. What is the greatest percentage discount on the listed price that avoids selling below cost?
3 marks

Read the worked solutions

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

Mark up a 30 AUD cost by 20%.
2 marks
$30 \times 1.2 = 36$ .
36 AUD
Discount a listed price of 90 AUD by 10%.
2 marks
$90 \times 0.9 = 81$ .
81 AUD
An item costs 48 AUD and is sold for 60 AUD. Find its dollar profit and percentage profit on cost.
3 marks
Profit: $60 - 48 = 12$ AUD.
$12 \div 48 \times 100 % = 25 %$ .
12 AUD; 25%
A listed price of 80 AUD is reduced by 15%. Find the sale price.
2 marks
$80 \times 0.85 = 68$ .
68 AUD
An item costs 80 AUD. It is marked up by 25%, then discounted by 10%. Find its final price and profit on cost.
4 marks
$80 \times 1.25 = 100$ .
$100 \times 0.9 = 90$ .
$90 - 80 = 10$ , and $10 \div 80 \times 100 % = 12.5 %$ .
90 AUD; 10 AUD profit or 12.5%
A store buys a book for 24 AUD and lists it at 30 AUD. What is the greatest percentage discount on the listed price that avoids selling below cost?
3 marks
The store may reduce the price by $30 - 24 = 6$ AUD.
$6 \div 30 \times 100 % = 20 %$ .
At 20% off, the sale price is exactly 24 AUD.
20%

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Curriculum reference & lesson scope

Australian Curriculum v9 / SA Curriculum

Percentage increase/decrease; finding an original amount; discounts and mark-ups; percentage comparisons; budgets and purchase decisions; modelling and checking financial problems with digital tools. Simple interest can be offered here as a school-dependent application and developed in Year 9.

Official curriculum source ↗

In this lesson

Understand the idea.

Keep the price stages separate

Compare profit and percentage language

See the method in action.

Mark up a cost

Find the mark-up amount.

Add the mark-up to the cost.

Check with a multiplier.

A sale can still make a profit

Calculate the listed price.

Apply the discount to that price.

Find the actual profit.

Express the profit relative to cost.

Try it yourself.

Check your understanding

Keep practising