Coaching Centre
Best buys, discounts and GST
Unit pricing to find the best buy, percentage discounts and mark-ups, successive discounts, working back to an original price, and adding or removing the 10% GST.
Supermarkets are designed to make comparing prices hard: different pack sizes, "2 for $\$7$" deals, specials on one size only. The maths in this section cuts through all of it. It's also the maths behind every GST question in the HSC.
Unit pricing
A unit price is the cost of a fixed amount, such as per 100 g, per litre or per item. Large supermarkets in Australia must show it on the shelf label, usually in small print under the main price. To compare products, compare unit prices, not shelf prices.
Ground coffee comes in a 200 g bag for $\$9.50$, a 500 g bag for $\$21$ and a 1 kg bag for $\$45$. Which is the best buy?
With no discount, check Example 1. How big a discount does the 1 kg bag need before it becomes the best buy?
Turn on the GST view. Check that GST is one eleventh of each price, and that the price before GST plus the GST gives the shelf price.
Discounts and mark-ups
A discount of $r\%$ multiplies the price by $(1 - r\%)$. A mark-up of $r\%$, which a shop adds to its cost price to make a profit, multiplies by $(1 + r\%)$. Using one multiplier is faster than finding the discount and subtracting it.
A jacket marked $\$120$ is reduced by $25\%$, and then a further $10\%$ is taken off at the register. Find the final price and the overall percentage discount.
To find an original price, divide by the multiplier. If a shirt costs $\$63$ after $25\%$ off, the original price was $63 \div 0.75 = \$84$.
GST
The goods and services tax is $10\%$, added to most goods and services in Australia. Basic food, most health and education services, and some other items are GST-free. Shelf prices in Australia must include GST.
- To add GST: multiply by $1.1$.
- To find the GST inside a price: divide by $11$. The price before GST is the price divided by $1.1$.
(a) A plumber quotes $\$240$ plus GST. Find the total. (b) A pair of shoes costs $\$86.90$ including GST. Find the GST and the price before GST.
Your turn
A shop buys a speaker for $\$40$ (before GST), marks it up $60\%$, then adds GST. Find the shelf price.
Show the working
Marked-up price: $40 \times 1.6 = \$64$. Add GST: $64 \times 1.1 = \$70.40$.
A 375 g box of cereal costs $\$4.50$. Find the price per 100 g.
$4.50 \div 375 \times 100 = \$1.20$ per 100 g.
Find the sale price of an $\$85$ item reduced by $30\%$.
$85 \times 0.70 = \$59.50$.
How much GST is included in a price of $\$132$?
$132 \div 11 = \$12$.
A service costs $\$450$ plus GST. Find the total price.
$450 \times 1.1 = \$495$.
Which is the best buy?
Per litre: $\$2.10$, $3.80 \div 2 = \$1.90$, $5.40 \div 3 = \$1.80$. The 3 L bottle is cheapest per litre.
A price is reduced by $20\%$, then the new price is reduced by $15\%$. What is the overall percentage discount?
$0.80 \times 0.85 = 0.68$, so you pay $68\%$. Overall discount: $100\% - 68\% = 32\%$.
A shop marks up an item costing $\$60$ by $45\%$. Find the selling price (ignore GST).
$60 \times 1.45 = \$87$.
After a $25\%$ discount, a shirt costs $\$63$. Find its original price.
Sale price $= 0.75 \times$ original, so original $= 63 \div 0.75 = \$84$.
Exam style: A textbook costs $\$59.40$ including GST. Find its price before GST.
$59.40 \div 1.1 = \$54$. Check: GST $= 59.40 \div 11 = \$5.40$, and $59.40 - 5.40 = 54$.
Exam style: A 1 kg bag of coffee is normally $\$45$. It is reduced by $20\%$. Find the new price per 100 g.
New price: $45 \times 0.80 = \$36$. Per 100 g: $36 \div 10 = \$3.60$.