Mathematics • Year 8 • Unit 1 • Lesson 19
Multi-Step Money — Real Scenarios
Apply markups, discounts, GST and bill-splitting to phone clearances, restaurant bills, depreciation, group dinners and clothing-store sales — then explain why "20% off, then 20% on" doesn't bring you back to where you started.
1. Word problems
Each problem chains together two or three financial moves. Use multipliers — show your working. A final answer with no working only earns half marks.
1.1 — Phone clearance. A retailer buys 50 phones at $200 each. They mark them up 30% for the retail price. They sell 40 at full retail and the last 10 at a 20% clearance discount.
(a) What is the retail price per phone?
(b) What is the clearance price per phone?
(c) What is the retailer's total revenue from all 50 phones? 3 marks
1.2 — Restaurant bill. A $176 inc-GST restaurant bill is split equally between 4 diners.
(a) How much GST is in the bill (use GST = total ÷ 11)?
(b) How much does each diner pay if the bill is split equally? 3 marks
1.3 — Car depreciation. A car worth $30 000 depreciates 20% in its first year, then another 15% in its second year.
(a) Find the multiplier for each year (e.g. −20% = × 0.80).
(b) Find the car's value at the end of year 2. 3 marks
1.4 — Group dinner. Six friends go to dinner. The bill comes to $216 inc-GST and they decide to split it in the ratio 1 : 1 : 1 : 2 : 2 : 3 (because some ate way more than others).
(a) What does each person pay?
(b) Check your shares add to $216. 3 marks
1.5 — Clothing-store sale. A clothing store buys 100 shirts at $25 each. They mark them up 80% for retail. On sale day they take 40% off retail and sell 60 shirts. The remaining 40 are sold at an even bigger clearance: another 50% off the SALE price.
(a) Find the retail price, the sale price and the clearance price.
(b) Calculate the total revenue from all 100 shirts. 3 marks
2. Explain your thinking
This question is about communication, not just answers. Use full sentences. 4 marks
2.1 A classmate says: "A $100 jacket gets marked up 20%, then comes back down 20% on sale. That brings it right back to $100, because +20 and −20 cancel out." Try this calculation yourself and show what really happens.
Then explain: (i) what answer you actually get, (ii) WHY the +20 and −20 don't cancel out (think about what each percentage is taken from), and (iii) write a single sentence rule for chained percentage changes. Use the phrase "different starting amounts" somewhere in your answer.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — Phone clearance
(a) Retail = $200 × 1.30 = $260.
(b) Clearance = $260 × 0.80 = $208.
(c) Total revenue = 40 × $260 + 10 × $208 = $10 400 + $2080 = $12 480.
1.2 — Restaurant bill ($176 inc-GST, split 4)
(a) GST = $176 ÷ 11 = $16.
(b) Each pays = $176 ÷ 4 = $44.
1.3 — Car depreciation
(a) Year 1: × 0.80 (−20%). Year 2: × 0.85 (−15%).
(b) $30 000 × 0.80 × 0.85 = $30 000 × 0.68 = $20 400.
1.4 — Group dinner $216 in 1 : 1 : 1 : 2 : 2 : 3
(a) Total parts = 10. 1 part = $216 ÷ 10 = $21.60. Shares: $21.60, $21.60, $21.60, $43.20, $43.20, $64.80.
(b) Check: 3 × $21.60 + 2 × $43.20 + $64.80 = $64.80 + $86.40 + $64.80 = $216 ✓.
1.5 — Clothing-store sale
(a) Retail = $25 × 1.80 = $45. Sale = $45 × 0.60 = $27. Clearance = $27 × 0.50 = $13.50.
(b) Total revenue = 60 × $27 + 40 × $13.50 = $1620 + $540 = $2160. (For context: total cost was 100 × $25 = $2500, so this actually made a loss of $340.)
2.1 — Explain your thinking (sample response)
The actual calculation gives $100 × 1.20 × 0.80 = $100 × 0.96 = $96, NOT $100. So a +20% / −20% chain leaves you 4% WORSE OFF, not back where you started.
The reason is that the two percentages are taken from different starting amounts. The +20% is taken from $100 (so it's worth $20), but the −20% is taken from $120 (so it's worth $24 — a bigger amount). Subtracting the bigger $24 from $120 lands you at $96, below the original $100.
The single-sentence rule: chained percentage changes are calculated as MULTIPLIERS multiplied together (1.20 × 0.80 = 0.96), not added and subtracted, because each new percentage is taken from a different starting amount.
Marking: 1 mark for the correct numerical answer ($96); 1 mark for explaining the different starting amounts; 1 mark for the multiplier rule; 1 mark for a clear, full-sentence explanation using "different starting amounts".