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Year 7AC9M7N09

Profit, Loss, Discount and GST

Use mathematical modelling to solve practical problems, involving rational numbers and percentages, including financial contexts.

Every money question in this topic is a percentage of an amount, then an addition or a subtraction. Naming which one you are doing is most of the work.

Builds onYr 7 · Percentage Increase and Decrease

Method

Profit and loss compare with the cost price
% profit=profitcost price×100\%\text{ profit} = \frac{\text{profit}}{\text{cost price}} \times 100
Always divide by what it cost, not what it sold for.
Discount is a decrease
sale price=price×(1−r)\text{sale price} = \text{price} \times (1 - r)
Same multiplier method as any percentage decrease.
GST is an increase of 10%
with GST=price×1,1\text{with GST} = \text{price} \times 1{,}1
To remove GST, divide by 1.1 — do not subtract 10%.

Worked example

e.g. A shop buys a bag for $40 and sells it for $50. Find the percentage profit.\text{A shop buys a bag for } \$40 \text{ and sells it for } \$50. \text{ Find the percentage profit.}
  1. Find the profit in dollars.50−40=1050 - 40 = 10
  2. Write it as a fraction of the cost price.1040\frac{10}{40}
  3. Multiply by 100 to get a percentage.1040×100=25%\frac{10}{40} \times 100 = 25\%
  4. State the answer in context.a 25% profit\text{a } 25\% \text{ profit}
  5. Check: 25% of the cost price should equal the profit.0,25×40=10✓0{,}25 \times 40 = 10 \quad\checkmark

Practice

Decide first whether it is an increase or a decrease.

1
Cost 80, sells for 100. Percentage profit?\text{Cost } 80, \text{ sells for } 100. \text{ Percentage profit?}
Answer25%25\%
2
Cost 250, sells for 200. Percentage loss?\text{Cost } 250, \text{ sells for } 200. \text{ Percentage loss?}
Answer20%20\%
3
A 60 item has 15% off. Sale price?\text{A } 60 \text{ item has } 15\% \text{ off. Sale price?}
Answer60×0,85=5160 \times 0{,}85 = 51
4
Add GST to $120\text{Add GST to } \$120
Answer120×1,1=132120 \times 1{,}1 = 132
5
A price including GST is $88. Find the price before GST.\text{A price including GST is } \$88. \text{ Find the price before GST.}
Answer88÷1,1=8088 \div 1{,}1 = 80
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