Mathematics • Year 10 • Unit 1 • Lesson 4
Discounts & Best Buys in the Real World
Apply discount, successive-discount, mark-up and unit-pricing tools from Lesson 4 to real Aussie shopping situations — Boxing Day sales, supermarket bulk packs, coffee shop margins, and the "two 20%s = 40%" trap. Then explain your method in your own words.
1. Word problems
Each problem uses a tool from Lesson 4: single discount, successive discount, mark-up, or unit-price comparison. Show your working — a final answer with no working only earns half marks.
1.1 — Boxing Day jacket. A puffer jacket is priced at $260 in November. On Boxing Day it is marked "40% off".
(a) Calculate the discount amount.
(b) Calculate the sale price two ways: first by subtracting, then by using the × 0.60 shortcut. 3 marks
1.2 — Two stacked discounts (the "40% trap"). A retailer advertises "30% off — plus another 20% off at the register". The original price of a couch is $1,500. A shopper assumes the total reduction is 50% and expects to pay $750.
(a) Calculate the actual price after both discounts are applied successively.
(b) How much more than $750 does the shopper actually pay?
(c) Express the actual total reduction as a single percentage. 3 marks
1.3 — Coffee shop margin. A café owner buys coffee beans for $32 per kilogram (cost price). She applies a 250% mark-up when she sells brewed coffee by weight.
(a) Calculate her selling price per kilogram.
(b) How much profit does she make per kilogram?
(c) What is her selling price per 100g? 3 marks
1.4 — Supermarket pasta comparison. Three pasta brands sit side-by-side on a Coles shelf:
- Brand X: 500g for $2.40
- Brand Y: 750g for $3.30
- Brand Z: 1kg for $4.80
(a) Calculate each unit price per 100g.
(b) Rank the three from cheapest to most expensive per 100g.
(c) Which is the best buy? 3 marks
1.5 — Working backwards from a sale price. Olivia sees a dress on sale for $84 after a 30% discount.
(a) Calculate the original price.
(b) Calculate the discount amount in dollars.
(c) Briefly explain why "$84 + 30% = original" is wrong as a method. 3 marks
2. Explain your thinking
This question is about communication, not just numbers. Use full sentences. 4 marks
2.1 A classmate says: "If two 20% discounts are applied one after another, that's the same as a single 40% discount, because 20 + 20 = 40." In your own words, explain (i) why this is wrong, (ii) what the actual combined reduction is (as a percentage), and (iii) demonstrate using a $500 jacket, comparing the price after successive 20% discounts with the price after a single 40% discount. Refer to "second discount is taken on the already-reduced price" somewhere in your explanation.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — Boxing Day jacket
(a) Discount = $260 × 0.40 = $104.
(b) Method 1: Sale = $260 − $104 = $156. Method 2: Sale = $260 × 0.60 = $156. $156.00 ✓.
1.2 — Two stacked discounts (the "40% trap")
(a) After 30% off: $1,500 × 0.70 = $1,050. After further 20% off: $1,050 × 0.80 = $840.00.
(b) Shopper expected $750; actual is $840. Difference = $90 more than expected.
(c) Combined reduction = ($1,500 − $840) ÷ $1,500 × 100 = $660 ÷ $1,500 × 100 = 44% off, not 50%.
Successive multipliers: 0.70 × 0.80 = 0.56, so 44% is removed — never simply 30 + 20.
1.3 — Coffee shop margin
(a) Selling = $32 × (1 + 2.50) = $32 × 3.50 = $112 per kg.
(b) Profit per kg = $112 − $32 = $80 per kg.
(c) Per 100g = $112 ÷ 10 = $11.20 per 100g.
1.4 — Pasta comparison
(a) Brand X: $2.40 ÷ 5 = $0.48/100g. Brand Y: $3.30 ÷ 7.5 = $0.44/100g. Brand Z: $4.80 ÷ 10 = $0.48/100g.
(b) Ranked cheapest to most expensive: Y ($0.44) < X ($0.48) = Z ($0.48).
(c) Brand Y is the best buy at $0.44 per 100g — interestingly, the middle-sized pack, not the largest.
The lesson warns: "a larger package is not always better value". This question proves it.
1.5 — Working backwards
(a) $84 is 70% of the original. Original = $84 ÷ 0.70 = $120.00.
(b) Discount = $120 − $84 = $36.
(c) "$84 + 30%" computes 30% of $84 = $25.20, giving $109.20 — that's not the original. The 30% in the discount was applied to the original price ($120), not the sale price ($84), so you can't reverse it by adding 30% of the sale.
2.1 — Explain your thinking (sample response)
My classmate is wrong because adding percentages only works when both percentages are applied to the same base. With successive discounts, the second discount is taken on the already-reduced price, not on the original — so a smaller dollar amount is removed in the second round. After a first 20% discount, 80% remains; the second 20% is taken from that 80%, leaving 64%. The actual combined reduction is therefore 36%, not 40%. Demonstration with a $500 jacket: after two successive 20% discounts the price is $500 × 0.80 × 0.80 = $320; after a single 40% discount the price is $500 × 0.60 = $300. The two are not equal — the successive approach leaves $20 more on the price.
Marking: 1 for naming the mistake; 1 for stating the correct combined % (36%); 1 for using the phrase "already-reduced price"; 1 for the $320 vs $300 demonstration.