Percentages · Usually met around P6
Sales tax
Tax = price × rate; with tax = price × (100% + rate).
How to do it
Method
Tax = price × rate; with tax = price × (100% + rate)
$200 plus 8% tax: 200 × 1.08 = 216
Another way
Tax first, then add the price
200 × 8100 = 16, 200 + 16 = 216
In full
In some places, sales tax is added to the price when you buy something. Sales tax = price × tax rate: $200 plus 8% sales tax, the tax is 200 × 8100 = $16, so you pay 200 + 16 = $216 in all. Or in one step: adding 8% means paying 100% + 8% = 108% of the price, and 108% as a decimal is 1.08 (not 1.8): 200 × 1.08 = 216. Going back from the total to the price: the total is 108% of the price, so 216 ÷ 108 × 100 = 200. Don't take 8% off the total, because the tax was worked out on the price.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
An item is priced at $370, plus 20% sales tax. How much is the sales tax?
Show the answer and working
Answer: 74 dollars
Tax = price × rate: 370 × 20100 = 74.
Example 2
An item is priced at $520. With 12% sales tax added, how much do you pay in all?
Show the answer and working
Answer: 582.4 dollars
The tax is 520 × 12100 = 62.4; 520 + 62.4 = 582.4.
Example 3
An item is priced at $450. With 20% sales tax added, you pay $360 in all.
True or false?
Show the answer and working
Answer: False
With tax you pay (100 + 20)% of the price: 450 × (100 + 20)/100 = 540.
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