Mathematics • Year 8 • Unit 1 • Lesson 7
Discounts and Sale Prices
Build fluency with the three quantities that show up at every shop sale: marked price, sale price, discount. Work forward (find the sale price), backward (find the marked price), and find the % off.
1. I do — fully worked example
Read every line. This is a REVERSE problem — given the sale price and the discount %, find the marked price.
Problem. A jacket is on sale for $84 after a 25% discount. What was the marked price?
Step 1 — Work out the pay-fraction.
25% off ⇒ you pay 75%, so pay-fraction = 1 − 0.25 = 0.75
Reason: the sale price represents 75% of the marked price.
Step 2 — Write the equation linking sale and marked.
Sale = Marked × 0.75 ⇒ 84 = M × 0.75
Reason: forward formula is Sale = Marked × (1 − rate). Plug in.
Step 3 — Rearrange: DIVIDE both sides by the pay-fraction.
M = 84 ÷ 0.75
Reason: reverse problems use DIVISION. Never just multiply by 0.75 again.
Step 4 — Compute and check.
M = $112. Check: 112 × 0.75 = $84 ✓
Reason: marked must be MORE than sale. Verify by multiplying back.
Answer: Marked price = $112. The shopper saved $28.
2. We do — fill in the missing steps
Same shape as Section 1, but with the working faded. Fill in each blank. 4 marks
Problem. A scarf is on sale for $42 after a 30% discount. What was the marked price?
Step 1 — Pay-fraction: 30% off ⇒ you pay ______%, so pay-fraction = ______.
Step 2 — Equation:
42 = M × ______
Step 3 — Divide to reverse:
M = 42 ÷ ______ = $______
Step 4 — Check by multiplying back:
______ × 0.70 = $______ ✓ Saving = $______
3. You do — independent practice
Show your working under each problem. The first four are foundation (forward — find the sale price). The middle two are standard (find % off). The last two are extension (reverse — find marked price).
Foundation — forward (find the sale price)
3.1 A $150 pair of jeans has 20% off. What is the sale price? 1 mark
3.2 A $240 marked guitar with 35% off. Find the sale price. 1 mark
3.3 A $76 marked top, 42% off. Sale price (round to the nearest cent)? 1 mark
3.4 A $1450 marked TV with 12% off. Find the sale price. 1 mark
Standard — find the % off
3.5 A $50 book is now on sale for $40. What percentage off is it? 2 marks
3.6 Saving $45 on a marked price of $150 — what % discount is that? 2 marks
Extension — reverse (find the marked price)
3.7 Sale price $108 after 10% off. What was the marked price? 2 marks
3.8 Tahlia paid $32 for a top that was on sale for 20% off. (a) What was the marked price? (b) How much did she save? 2 marks
How did this worksheet feel?
What I'll revisit before next class:
Section 2 — We do ($42 at 30% off)
Step 1: You pay 70%; pay-fraction = 0.70.
Step 2: 42 = M × 0.70.
Step 3: M = 42 ÷ 0.70 = $60.
Step 4 check: 60 × 0.70 = $42 ✓. Saving = $18.
3.1 — $150 jeans, 20% off
Sale = 150 × 0.80 = $120.
3.2 — $240 guitar, 35% off
Sale = 240 × 0.65 = $156.
3.3 — $76 top, 42% off
Sale = 76 × 0.58 = $44.08.
3.4 — $1450 TV, 12% off
Sale = 1450 × 0.88 = $1276.
3.5 — $50 book, sale $40
Saving = 50 − 40 = $10. % off = (10 / 50) × 100 = 20% off.
3.6 — Save $45 on $150
% off = (45 / 150) × 100 = 30% off.
3.7 — Sale $108 after 10% off
Pay-fraction = 0.90. Marked = 108 ÷ 0.90 = $120. (Check: 120 × 0.90 = $108 ✓.)
3.8 — Tahlia paid $32 (20% off)
(a) Marked = 32 ÷ 0.80 = $40.
(b) Saved = 40 − 32 = $8.