Mathematics • Year 10 • Unit 1 • Lesson 4
Discounts, Mark-ups & GST — Mixed Challenge
Pull together every percentage idea from Lessons 3-4: discounts, successive discounts, mark-ups, unit-price comparisons, and GST add/extract. Choose the right tool for each problem, spot someone else's mistake, then design a retail price tag and sale promotion of your own.
1. Mixed problems — choose the right tool
Each question uses a different percentage idea from Lessons 3-4. Decide which formula applies before you start writing. Show your working. 3 marks each
1.1 A handbag is reduced from $260 to $182. What percentage discount has been applied?
1.2 A retailer buys T-shirts for $14 cost price and marks them up 175%. Find the selling price.
1.3 An olive oil bottle (750mL) costs $14.25. Another bottle (1L) costs $17.60. Which is the better buy per 100mL?
1.4 A laptop is advertised as "25% off, plus an extra 10% off at the checkout". The original price is $1,800. Find the final price.
1.5 A pair of sneakers has a sale tag of $96 after a 20% discount. Find the original price.
1.6 A bookstore buys a paperback for $18 cost price, marks it up by 60%, and the customer is charged GST on top of the marked-up price. Find the GST-inclusive total the customer pays.
2. Find the mistake
Another student has tried to calculate the final price of a $400 jacket after a "30% off, then a further 15% off" promotion. 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 — $400 jacket, 30% then 15% off:
Line 1: Total discount = 30% + 15% = 45%
Line 2: Discount amount = $400 × 0.45 = $180
Line 3: Sale price = $400 − $180 = $220
Line 4: Final price the customer pays = $220.
(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 final answer.
Stuck? The lesson explicitly warns: percentage discounts cannot simply be added. Look at Line 1.3. Open-ended challenge — design a price tag
This question has many valid answers. Be realistic, but show every number. 4 marks
3.1 You are the owner of a small Australian online clothing store. You buy hoodies wholesale for $25 cost price. Design a complete pricing plan that satisfies all of the following:
- A mark-up of between 120% and 180% applied to cost.
- 10% GST added on top of the marked-up price to give a shelf price.
- A sale promotion that takes 25% off the shelf price.
- The final sale price must still leave a profit (i.e. exceed the $25 cost price).
Show:
(i) Your chosen mark-up percentage and the marked-up price.
(ii) The GST amount and the shelf price (mark-up + GST).
(iii) The sale price after the 25% discount.
(iv) The profit per hoodie sold at the sale price (sale price − cost − GST that you still owe the ATO).
Tip: GST owed to the ATO = sale price ÷ 11.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — Discount % from prices
Discount amount = $260 − $182 = $78. Discount % = ($78 ÷ $260) × 100 = 30%.
1.2 — T-shirt mark-up
Selling = $14 × (1 + 1.75) = $14 × 2.75 = $38.50.
1.3 — Olive oil best buy
750mL bottle: 750 ÷ 100 = 7.5 units of 100mL. $14.25 ÷ 7.5 = $1.90 per 100mL.
1L bottle: 1000 ÷ 100 = 10 units. $17.60 ÷ 10 = $1.76 per 100mL.
1L bottle is the better buy by $0.14 per 100mL.
1.4 — Successive discounts on laptop
After first discount: $1,800 × 0.75 = $1,350.
After second discount: $1,350 × 0.90 = $1,215.00.
If a customer assumed 35% off, they'd expect $1,170 — they actually pay $45 more.
1.5 — Original from sale price
$96 = 80% of original. Original = $96 ÷ 0.80 = $120.
1.6 — Paperback with mark-up and GST
Marked-up = $18 × 1.60 = $28.80.
GST = $28.80 × 0.10 = $2.88.
GST-inclusive total = $28.80 + $2.88 = $31.68 (or $28.80 × 1.10).
Note: in practice many books are GST-free or have GST built into the shelf price — this is an exercise in stacking operations.
2 — Find the mistake
(a) The mistake is on Line 1.
(b) Percentage discounts cannot be added when applied successively, because the second percentage is taken from the already-reduced price, not the original. 30% + 15% = 45% would only be valid if both percentages applied to the same starting price.
(c) Corrected working:
After first 30% off: $400 × 0.70 = $280.
After second 15% off: $280 × 0.85 = $238.00.
Final price = $238.00, not $220.
The wrong "added" approach undercharges by $18 — bad for the retailer, looks like a bigger discount than it is for the customer.
3 — Open-ended challenge (sample pricing plan)
Mark-up: 150% (within the 120-180% range).
Marked-up price = $25 × (1 + 1.50) = $25 × 2.50 = $62.50.
Add GST:
GST = $62.50 × 0.10 = $6.25.
Shelf price = $62.50 + $6.25 = $68.75 (or $62.50 × 1.10).
Sale promotion (25% off):
Sale price = $68.75 × 0.75 = $51.56 (to nearest cent).
Profit per hoodie at sale price:
GST owed to ATO = $51.56 ÷ 11 ≈ $4.69 (1/11 of the GST-inclusive sale price).
Net to retailer = $51.56 − $4.69 = $46.87.
Profit = $46.87 − $25 = $21.87 per hoodie.
Marking: 1 for valid mark-up in range with correct calculation; 1 for GST add to give shelf price; 1 for correct sale-price calculation; 1 for profit > $0 after backing out GST owed. Any plan satisfying the constraints earns full marks.