Mathematics • Year 8 • Unit 1 • Lesson 7
Sale Tags in the Real World
Work through realistic discount problems: shop sales, layered discounts, sale-to-marked reversals and "save $X" headlines. Then explain why a discount-then-markup does NOT bring you back to the original.
1. Word problems
Each problem involves a marked price, sale price, or discount. Show your working — single final answers with no working earn only half marks.
1.1 — Black Friday TV. A 55-inch TV is marked at $1200. On Black Friday it is 40% off.
(a) Find the discount in dollars.
(b) Find the sale price using the multiplier method.
(c) Confirm: sale + saving = marked. 3 marks
1.2 — Sale-tag mystery. A pair of headphones is on sale for $76.50 after a 15% discount.
(a) Work out the original (marked) price.
(b) How much did the shopper save? 3 marks
1.3 — "Half-price" hoodie. A hoodie marked at $80 has a sticker that says "Half price — only $40!".
(a) Convert the "half price" claim into a % discount.
(b) Verify that 80 × (1 − 0.50) really does give $40.
(c) The shop later raises the sale price to $44, claiming "Still on sale!". What new % discount is now on offer? 3 marks
1.4 — Concert ticket bundle. A two-ticket bundle for a concert is marked at $220 in advance but is sold at the door for $176.
(a) What is the door discount in dollars?
(b) Convert that into a percentage discount off the marked price.
(c) The promoter wants to advertise the discount on a poster — would you put "save $44" or "20% off"? Briefly say which is more eye-catching and why. 3 marks
1.5 — Member's bonus. A new mountain bike has a marked price of $1800. Members receive a 25% discount, and on Mondays members get an extra 10% off the already-discounted price.
(a) What does a member pay for the bike on a Monday?
(b) A non-member pays the full $1800. How much does a Monday member save in total? 3 marks
2. Explain your thinking
This question is about communication, not just answers. Use full sentences. 4 marks
2.1 A guitar shop normally sells a guitar for $480. During a winter sale it is reduced by 25%. After the sale ends, the shop adds a 20% markup to the sale price to "go back to normal pricing". A customer says "25% off then 20% on must bring it back to $480 — that's a fair sale, but it ends up where it started." Show that this is WRONG.
In your answer, calculate (i) the sale price after the 25% discount, (ii) the post-sale price after the 20% markup is added to the sale price, and (iii) compare to $480. Then explain in one or two sentences why the discount and markup do NOT cancel out. Use the phrase "different base prices" somewhere.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — $1200 TV, 40% off
(a) Discount = 0.40 × 1200 = $480.
(b) Sale = 1200 × 0.60 = $720.
(c) Check: 720 + 480 = $1200 ✓.
1.2 — Headphones at $76.50 after 15% off
(a) Marked = 76.50 ÷ 0.85 = $90.
(b) Saving = 90 − 76.50 = $13.50.
1.3 — $80 hoodie, half price = $40
(a) Half price means 50% off.
(b) 80 × (1 − 0.50) = 80 × 0.50 = $40 ✓.
(c) New sale price $44: saving = 80 − 44 = $36. % off = (36 / 80) × 100 = 45% off.
1.4 — Concert ticket, $220 → $176 at door
(a) Discount = 220 − 176 = $44.
(b) % off = (44 / 220) × 100 = 20%.
(c) Sample answer: "20% off" usually sounds more eye-catching because it scales — a higher % feels like a bigger deal regardless of original price. But "save $44" is a concrete dollar amount, which appeals to shoppers who think in dollars rather than percentages. Both describe the same deal.
1.5 — $1800 bike, member 25% then extra 10% on Monday
(a) Final price = 1800 × 0.75 × 0.90 = 1350 × 0.90 = $1215.
(b) Total saving = 1800 − 1215 = $585. (Not the same as "35% off" — that would be $1170.)
2.1 — Explain your thinking (sample response)
(i) Sale price after 25% off = 480 × 0.75 = $360.
(ii) Post-sale price after 20% markup on the sale price = 360 × 1.20 = $432.
(iii) $432 is NOT $480 — the customer is wrong by $48.
The 25% discount and 20% markup do NOT cancel because they act on different base prices. The 25% off is taken from the original $480 ($120 saved), while the 20% markup is added to the smaller post-discount $360 (only $72 added). When the percentages are applied to different base prices, they don't offset evenly — leaving the final price below the original. In fact, the net effect is equivalent to a single 10% discount on the original ($432 is 10% less than $480).
Marking: 1 mark for the $360 sale price; 1 mark for the $432 post-markup price; 1 mark for stating the customer is wrong (not $480); 1 mark for a clear explanation that uses "different base prices".