Work through the levels in order. Type your answer and press Check — open the worked solution if you get stuck. Answers like -6, 3/4 or 0.25 are typed exactly as shown. A ⭐ Bonus Challenge at the end is extra credit — skip it if the rest was hard work.
Level 1 · Warm-up
1 Juice is sold in two sizes. Which is the better buy, and what is its price per litre?
Show worked solution
$4.20 ÷ 1.5 = $2.80 per litre. 600 mL = 0.6 L, and $1.80 ÷ 0.6 = $3.00 per litre. Better buy: 1.5 L at $2.80 per litre.
2 A plumber charges $240 for labour and a $35 call-out fee, both before GST. Find the GST and the total bill including GST.
Show worked solution
240 + 35 = $275. GST = 10% of 275 = $27.50. Total = 275 × 1.1 = $302.50.
3 Muesli bars come in a box of 6 for $4.50 or a box of 15 for $10.50. At the better unit price, how many bars can you buy for $21?
Show worked solution
Box of 6: $0.75 a bar. Box of 15: $0.70 a bar, the better buy. 21 ÷ 0.70 = 30 bars (two boxes of 15).
Level 2 · Core
4 A receipt shows a total of $396 including GST. What was the price before GST?
Show worked solution
396 ÷ 1.1 = $360. Check: 360 × 1.1 = 396. ($356.40 takes 10% off the inclusive total; $36 is the GST; $435.60 adds GST again.)
5 Shoes priced at $160 are 25% off, and a further 5% is taken off the sale price at the checkout. Find the price paid and the single equivalent discount.
Show worked solution
160 × 0.75 = 120, and 120 × 0.95 = $114. One multiplier: 0.75 × 0.95 = 0.7125, so you pay 71.25%: 28.75% off (not 30%).
6 Batteries come in packs of 12 for $15 or packs of 20 for $24, and you can only buy whole packs. With $72, how many more batteries do you get by buying only 20-packs than by buying only 12-packs?
Show worked solution
20-packs: 72 ÷ 24 = 3 packs = 60 batteries. 12-packs: 72 ÷ 15 = 4.8, so 4 packs = 48 batteries. 60 − 48 = 12 more.
Level 3 · Challenge
7 A jacket costs $200 before GST. It is discounted by 25%, and GST is then added.1 Adding GST first and discounting second gives the same final price, $165.
2 The GST paid is $15.
3 $165 is 15% less than the full price with GST, $220.
Which statements are correct?
2 The GST paid is $15.
3 $165 is 15% less than the full price with GST, $220.
Which statements are correct?
Show worked solution
200 × 0.75 × 1.1 = 200 × 1.1 × 0.75 = $165 (1 ✓). GST is 10% of the discounted $150: $15 (2 ✓). 165 ÷ 220 = 0.75, so $165 is 25% less, not 15% (3 ✗). 1 and 2.
8 A $480 bike is reduced by 12.5%. At the register a further discount brings the price to $315. Find the sale price after the first discount, and the size of the second discount.
Show worked solution
480 × 0.875 = $420. 315 ÷ 420 = 0.75, so the second discount is 25% off. (Comparing with $480 gives 315 ÷ 480 = 0.65625 — the overall discount, not the second one.)
9 A clearance item starts at $625. At the end of each week its price is cut by 40% of its current price. After how many weeks is the price first below $100?
Show worked solution
625 → 375 → 225 → 135 → 81. After 3 weeks it is $135; after 4 weeks it is $81, the first price below $100. (Taking $250 off each week, 40% of the starting price, would wrongly make it 3 weeks.)