GST
The Howard Government reformed the then state and federal run sales tax system in 2000 by introducing the Goods and Services Tax, or GST. It is a value-added tax, usually of $10%$10%, on most goods and services transactions. In other words, the prices businesses charge you include an additional $10%$10% of the original price as a GST amount. For example, if the original price of an item was $\$10$$10, the GST on this item $\$1$$1 since $10%$10% of $\$10$$10 is $\$1$$1. The price you would be charged would be $\$11$$11 since $10+1=11$10+1=11. The GST is given to the government by the business therefore they need to keep track of how much GST they pay and receive. So it is important to be able to calculate prices before and after GST, as well as the amount and rate of GST.
To calculate the price of an item after GST is added we multiply by $1.1$1.1
To calculate the original price of an item before GST if we know the final price including GST we divide by $1.1$1.1
Worked example
Example 1
Aaron received a bill of $\$68$$68 for consultation and $\$10$$10 for herbal supplements from a medical professional. If GST is only applied to the consultation fee, what is the total bill that Aaron must pay? Give your answer correct to two decimal places.
Think: GST is an additional $10%$10% of the cost.
Do: Consultation increased by $10$10% GST: $68\times1.1=\$74.80$68×1.1=$74.80
Herbal supplements: $\$10$$10 (we don't need to change this amount as the GST only applies to the consultation.
Total: $74.80+10=\$84.80$74.80+10=$84.80
Reflect: We could also work this out in one step:
$68\times1.1+10=\$84.80$68×1.1+10=$84.80
Practice questions
Question 1
Calculate the GST-included sales price for an item with an original price of $\$20$$20.
Question 2
The sales price of an item, including GST, is $\$40$$40. Calculate the price of the item without GST.
Round your answer to the nearest cent.