Mathematics • Year 8 • Unit 1 • Lesson 6
Percentage Decrease in the Real World
Use percentage decrease where it shows up in real life: shop sales, depreciation on cars and phones, end-of-season clearance and family-size reductions. Then explain your thinking on the classic "double-discount" trap.
1. Word problems
Each problem uses a percentage decrease. Show your working — a single final answer with no working only earns half marks.
1.1 — End-of-season sneakers. A $180 pair of sneakers is reduced by 35% in an end-of-season clearance.
(a) What is the discount in dollars?
(b) What is the sale price (use the multiplier method)? 3 marks
1.2 — Brand-new car loses value. A new car worth $40 000 depreciates by 15% in its first year on the road.
(a) How much value (in dollars) does it lose in year 1?
(b) What is the car worth at the end of year 1? 3 marks
1.3 — Family discount on a meal. A family meal package is normally priced at $85. The restaurant offers a 22% Tuesday-night family discount.
(a) Work out the discount in dollars (round to the nearest cent).
(b) What is the price the family pays on Tuesday night? 3 marks
1.4 — Phone trade-in. A phone is worth $1200 brand new. It loses 25% of its value each year for the first two years.
(a) What is it worth at the end of year 1?
(b) Apply the 25% decrease AGAIN to that figure to find the value at the end of year 2.
(c) After 2 years, what total percentage of its original value has been lost? 3 marks
1.5 — "Save $$" sale tag. A $240 jumper is marked "35% off — save big!" Show two ways to find the sale price: (a) the subtract method (find the discount, then subtract) and (b) the multiplier method (× 0.65). Confirm both give the same answer. 3 marks
2. Explain your thinking
This question is about communication, not just answers. Use full sentences. 4 marks
2.1 Store A offers "25% off, then a further 10% at the checkout" on a $200 jacket. Store B offers "30% off everything" on the same $200 jacket. A classmate says "25% plus 10% equals 35%, so Store A is the better deal."
In your own words, explain (i) what the final price is at each store (show working), (ii) which is actually cheaper, and (iii) why "25% plus 10%" does NOT equal "35% off". Use the phrase "the second discount is applied to the already-discounted price" somewhere in your answer.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — Sneakers at 35% off $180
(a) Discount = 0.35 × 180 = $63.
(b) Sale = 180 × 0.65 = $117 (or 180 − 63 = $117). ✓
1.2 — $40 000 car, 15% depreciation
(a) Loss = 0.15 × 40 000 = $6000.
(b) End of year 1 = 40 000 × 0.85 = $34 000.
1.3 — $85 family meal, 22% Tuesday discount
(a) Discount = 0.22 × 85 = $18.70.
(b) Price paid = 85 − 18.70 = $66.30 (or 85 × 0.78 = $66.30).
1.4 — Phone losing 25% per year
(a) End of year 1: 1200 × 0.75 = $900.
(b) End of year 2: 900 × 0.75 = $675.
(c) Total lost = 1200 − 675 = $525. As a percentage: 525 / 1200 × 100 = 43.75% — NOT 50%. Two 25% drops in a row don't add cleanly because the second one acts on the smaller, year-1 value.
1.5 — $240 jumper at 35% off, two ways
(a) Subtract method: discount = 0.35 × 240 = $84. Sale = 240 − 84 = $156.
(b) Multiplier method: 240 × 0.65 = $156. Both give the same answer. ✓
2.1 — Explain your thinking (sample response)
Store A's price: 200 × 0.75 × 0.90 = $150 × 0.90 = $135. Store B's price: 200 × 0.70 = $140. So Store A is actually cheaper, by $5. However, the classmate's reasoning is wrong even though they got the right "cheaper" answer for the wrong reasons. "25% plus 10%" does NOT equal "35% off" because the second discount is applied to the already-discounted price, not to the original $200. The 10% comes off $150, not $200, so it only saves $15 — making the total savings $50 + $15 = $65 (32.5%), not the full $70 (35%). The Store B deal of "30% off everything" saves $60, slightly less than Store A's actual saving of $65.
Marking: 1 mark for correct Store A price ($135); 1 mark for correct Store B price ($140); 1 mark for stating Store A is cheaper by $5; 1 mark for a clear explanation that the second 10% applies to the already-discounted price.