Mathematics • Year 8 • Unit 1 • Lesson 9

Profit and Loss in the Real World

Apply profit and loss to genuine small-business situations: school canteens, market stalls, second-hand selling, and flower stalls with wastage. Then explain why "unsold stock" still counts as a cost.

Apply · Real-World Maths

1. Word problems

Each problem is a real small-business scenario. Show your working — single answers without working only earn half marks.

1.1 — Second-hand phone resale. Mia buys a used iPhone for $200 to flip on Marketplace. She lists it for $260 and a buyer offers $245, which she accepts.

(a) What was her selling price?
(b) Did she make a profit or a loss?
(c) How much, in dollars? 3 marks

Stuck? SP = $245, CP = $200. Compare and subtract.

1.2 — School canteen lunch. The canteen buys 50 wraps from the supplier at $3 each. They sell 40 wraps at $6 each over lunch break; 10 are left unsold and given to staff for free.

(a) Total CP of all 50 wraps?
(b) Total SP from the 40 sold wraps?
(c) Total profit (or loss) for the canteen on wraps that day? 3 marks

Stuck on (c)? Don't forget the 10 unsold wraps still cost the canteen $3 each.

1.3 — Garage sale. The Patel family sells four items at a Saturday garage sale:
• bookshelf — originally bought for $80, sold for $30
• bike — originally bought for $200, sold for $250
• lamp — originally bought for $40, sold for $5
• boardgame set — originally bought for $25, sold for $25

(a) For EACH item, state profit, loss, or break-even and the dollar amount.
(b) What is the family's OVERALL profit or loss across all four items? 3 marks

Stuck? Compute each item separately, then sum the profits (positive) and losses (negative).

1.4 — Bakery batch. Daniel the baker makes 100 loaves of bread. Ingredients and electricity cost him $200 total. He sells 80 loaves at $3.50 each. The remaining 20 loaves go stale and are thrown out (sold for $0).

(a) Total CP?
(b) Total SP?
(c) Profit or loss, and the dollar amount?
(d) If he could have sold ALL 100 loaves, what would his profit have been? 3 marks

Stuck on (d)? SP if all 100 sold = 100 × 3.50 = $350. Then profit = $350 − $200.

1.5 — Reverse-engineer the cost. A reseller sells a vintage skateboard at $180 and makes a $45 profit on the sale.

(a) What was the cost price?
(b) If the buyer had only offered $120, would the reseller have made a profit or a loss?
(c) Find the dollar amount of that profit or loss. 3 marks

Stuck on (a)? CP = SP − profit. Then compare CP to the alternative $120 offer.

2. Explain your thinking

This question is about communication, not just answers. Use full sentences. 4 marks

2.1 A flower seller buys 200 bouquets at $4 each. They sell 150 at $10, 30 at a discounted price of $6, and the remaining 20 wilt and are thrown out.

In your answer: (i) calculate total CP, (ii) calculate total SP, (iii) determine total profit or loss, (iv) explain in one or two sentences why the 20 wilted bouquets are a hidden cost to the seller even though they were "free" once they wilted. Use the phrase "unsold stock is still cost recovered as nothing" somewhere in your answer.

Stuck? Total CP = 200 × 4. Total SP = 150 × 10 + 30 × 6 + 20 × 0. The 20 wilted bouquets cost $80 worth of CP that the seller never got back.

How did this worksheet feel?

Got it Partly Lost

What I'll revisit before next class:

Answers — Do not peek before attempting

1.1 — Mia's phone resale

(a) SP = $245. (b) SP > CP ($245 > $200), so PROFIT. (c) Profit = 245 − 200 = $45 profit.

1.2 — Canteen wraps

(a) Total CP = 50 × 3 = $150 (all 50, even the unsold).
(b) Total SP = 40 × 6 = $240.
(c) Profit = 240 − 150 = $90 profit.

1.3 — Patel garage sale

(a) Bookshelf: 30 − 80 = $50 LOSS. Bike: 250 − 200 = $50 PROFIT. Lamp: 5 − 40 = $35 LOSS. Boardgame: 25 − 25 = BREAK-EVEN.
(b) Total = $50 profit + ($50 loss + $35 loss) = $50 − $85 = $35 loss overall.

1.4 — Daniel's bakery

(a) Total CP = $200.
(b) Total SP = 80 × 3.50 + 20 × 0 = $280.
(c) Profit = 280 − 200 = $80 profit.
(d) If all 100 sold: SP = 100 × 3.50 = $350. Profit = 350 − 200 = $150. So wastage cost Daniel $70 in lost profit.

1.5 — Vintage skateboard reseller

(a) CP = SP − profit = 180 − 45 = $135.
(b) $120 < $135, so it would have been a LOSS.
(c) Loss = 135 − 120 = $15 loss.

2.1 — Explain your thinking (sample response)

(i) Total CP = 200 × 4 = $800.
(ii) Total SP = 150 × 10 + 30 × 6 + 20 × 0 = 1500 + 180 + 0 = $1680.
(iii) Profit = 1680 − 800 = $880 profit.
(iv) The 20 wilted bouquets are a hidden cost because the seller paid $4 each for them ($80 worth) but received nothing back when they couldn't sell them — unsold stock is still cost recovered as nothing. If those 20 bouquets had sold at the regular $10 price, the seller would have earned an extra $200 and brought total profit to $1080. So the wastage didn't just stop new income — it permanently absorbed $80 of cost that the seller paid for nothing.

Marking: 1 mark for $800 CP; 1 mark for $1680 SP; 1 mark for $880 profit; 1 mark for a clear explanation that uses "unsold stock is still cost recovered as nothing" or equivalent reasoning about hidden cost of wastage.