Mathematics • Year 8 • Unit 1 • Lesson 8
GST — Mixed Challenge
Pull together everything from Lesson 8: adding GST, stripping GST, the 1/11 shortcut, GST-free items, and mixed receipts. Six mixed problems, one "find the mistake" on an inc-GST calculation, and one open-ended challenge.
1. Mixed problems — choose the right move
Each question uses a different combination of ideas from Lesson 8. Decide whether you are adding, stripping, or using the 1/11 shortcut before you start writing. Show your working. 3 marks each
1.1 An item costs $240 exc-GST. Find the inc-GST price.
1.2 A receipt total is $77 inc-GST. Find the GST amount and the exc-GST price.
1.3 A receipt total is $165 inc-GST. What was the exc-GST price?
1.4 A bakery's exc-GST takings for a Sunday are $300 from non-bread items (taxable). What inc-GST total did the customers actually pay?
1.5 A grocery basket totals $46.20 inc-GST. Of that, $24 was for GST-free fresh fruit and bread. (a) Find the inc-GST total for the taxable items only. (b) Find the GST included in the taxable subtotal.
1.6 A restaurant meal is advertised at $25 exc-GST. (a) Inc-GST price? (b) If the bill includes one meal AND one $4.40 inc-GST drink, what is the total bill AND the total GST?
2. Find the mistake
A Year 8 student tried to find the GST included in a receipt total of $110 inc-GST. Their working is shown below. Exactly one line contains a mistake. Spot it, explain why it's wrong, then re-do the working correctly. 3 marks
Student's working — GST inside $110 inc-GST receipt:
Line 1: GST is 10%, so I take 10% of the receipt total.
Line 2: GST = 0.10 × 110 = $11.
Line 3: So exc-GST price = 110 − 11 = $99.
Line 4: Check: 99 × 1.10 = $108.90 — close to $110 so it must be right.
(a) Which line contains the mistake?
(b) Explain in one or two sentences why that line is wrong.
(c) Write out the corrected working in full, including the corrected GST amount and exc-GST price.
Stuck? 10% is taken from the EXC-GST price, not the inc-GST total. On an inc-GST total, the GST is 1/11 — not 1/10.3. Open-ended challenge — receipt detective
This question has more than one valid answer. 4 marks
3.1 Your task: design a realistic supermarket receipt that totals exactly $110 inc-GST, has at least 5 items, and contains BOTH GST-free items and taxable items.
For full marks your receipt must:
(i) List each item with its inc-GST price and a clear "GST" or "GST-free" label.
(ii) Add up to exactly $110.
(iii) Include a calculation of the TOTAL GST you actually paid (only on the taxable items).
(iv) State what percentage of the $110 total was GST (round to 1 dp).
Hint: Bread, fresh fruit, milk, vegetables are typical GST-free items. Chocolate, drinks, magazines, household items are typical taxable items. Taxable items must end in clean inc-GST amounts you can divide by 11.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — $240 exc-GST
Inc-GST = 240 × 1.10 = $264.
1.2 — Receipt $77 inc-GST
GST = 77 ÷ 11 = $7. Exc-GST = 77 − 7 = $70 (or 77 ÷ 1.10 = $70).
1.3 — Receipt $165 inc-GST
Exc-GST = 165 ÷ 1.10 = $150.
1.4 — Bakery $300 exc-GST takings
Inc-GST takings = 300 × 1.10 = $330.
1.5 — $46.20 basket with $24 GST-free
(a) Taxable subtotal = 46.20 − 24 = $22.20.
(b) GST = 22.20 ÷ 11 = $2.02 (rounded to nearest cent; exact = $2.0181…).
1.6 — $25 exc-GST meal + $4.40 inc-GST drink
(a) Meal inc-GST = 25 × 1.10 = $27.50.
(b) Total bill = 27.50 + 4.40 = $31.90. Total GST = (27.50 ÷ 11) + (4.40 ÷ 11) = $2.50 + $0.40 = $2.90.
2 — Find the mistake
(a) The mistake is on Line 1 (and the wrong base is then used in Line 2). The student also missed that the Line 4 check disproves the answer — 99 × 1.10 ≠ 110, so the working can't be right.
(b) GST is 10% of the EXC-GST price, not 10% of the inc-GST total. On an inc-GST total, the GST is 1/11 of the total — not 1/10. Taking 10% of $110 gives $11, but $11 is too much (the GST is actually $10).
(c) Corrected working:
GST = 110 ÷ 11 = $10.
Exc-GST = 110 − 10 = $100 (or 110 ÷ 1.10 = $100).
Check: 100 × 1.10 = $110 ✓.
3 — Open-ended challenge (sample receipt)
Sample receipt totalling exactly $110:
Bread loaf $4.00 (GST-free)
Milk 2 L $5.00 (GST-free)
Fresh apples 1 kg $7.50 (GST-free)
Carrots 1 kg $3.50 (GST-free)
Eggs 12 pack $7.00 (GST-free)
Bananas $3.00 (GST-free)
Subtotal GST-free = $30.00
Shampoo $11.00 (inc-GST)
Chocolate bar $2.75 (inc-GST)
Drink 600 mL $5.50 (inc-GST)
Magazine $9.90 (inc-GST)
Dishwashing liquid $7.70 (inc-GST)
Hand soap $6.60 (inc-GST)
Tissues $4.40 (inc-GST)
Detergent $11.00 (inc-GST)
Toothpaste $11.00 (inc-GST)
Air freshener $10.15 (inc-GST)
Subtotal taxable inc-GST = $80.00
TOTAL = 30 + 80 = $110 ✓
Total GST = 80 ÷ 11 ≈ $7.27. Percentage of receipt that is GST = (7.27 / 110) × 100 ≈ 6.6%. (Less than 10% because nearly a third of the basket was GST-free.)
Marking: 1 mark for a receipt that totals exactly $110 with at least 5 items; 1 mark for clear GST-free vs taxable labels; 1 mark for a correct total GST calculation (applied only to taxable items); 1 mark for the GST-as-% of total. Multiple valid receipts possible — markers should verify the arithmetic only.