Mathematics • Year 8 • Unit 1 • Lesson 10
Percentage Profit and Loss in the Real World
Use percentage profit and loss to compare deals fairly: bakeries setting prices, used-car traders, brand A vs brand B per-unit profit, and the difference between dollar profit and percentage margin.
1. Word problems
Each problem uses percentage profit or loss in a realistic business situation. Show your working — single final answers with no working only earn half marks.
1.1 — Bakery markup. A bakery's croissants cost $1.50 each to make (CP). They sell them for $3.75 each (SP).
(a) Dollar profit per croissant?
(b) Percentage profit on cost?
(c) Is this called a "markup" or a "discount"? Briefly say which. 3 marks
1.2 — Used-car loss. A car dealer buys a used hatchback for $15 000 and sells it after a week for $12 000.
(a) Dollar loss?
(b) Percentage loss on cost?
(c) The dealer's manager says "lose 20% on this deal — at least we got rid of it". Verify the manager's percentage. 3 marks
1.3 — Set a price for a target profit. A bakery wants a 30% profit on its $8 CP cakes.
(a) What SP should they set?
(b) What is the profit per cake in dollars?
(c) If they instead sold each cake for $11.20, what would the percentage profit be? 3 marks
1.4 — Phone trade-in loss. Maya bought a phone for $1500 two years ago. She trades it in today for a credit of $450 against a new model.
(a) Dollar loss on the original phone?
(b) Percentage loss on cost?
(c) What percentage of the original cost did Maya recover (i.e. the trade-in as a % of CP)? 3 marks
1.5 — Pen wholesaler. A wholesaler buys pens for $1.20 each and wants a 25% profit on cost.
(a) Find the SP per pen.
(b) If a customer buys 80 pens, what is the total revenue and the total profit?
(c) If the wholesaler raises their target to 50% profit on cost, what new SP per pen should they charge? 3 marks
2. Explain your thinking
This question is about communication, not just answers. Use full sentences. 4 marks
2.1 Two clothing brands sell similar shirts. Brand A makes $15 profit on each shirt with CP $30. Brand B makes $20 profit on each shirt with CP $80. A friend says "Brand B is making more money per shirt, so Brand B has the better margin".
In your answer: (i) calculate % profit for each brand, (ii) state which brand has the higher percentage profit per shirt, (iii) explain in one or two sentences why a higher dollar profit doesn't always mean a better margin. Use the phrase "% profit measures efficiency per dollar invested" somewhere.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — Bakery croissants $1.50 → $3.75
(a) Profit = 3.75 − 1.50 = $2.25 per croissant.
(b) % profit = (2.25/1.50) × 100 = 150% profit on cost.
(c) Markup — the bakery is selling above cost by 150%.
1.2 — Used car $15 000 → $12 000
(a) Loss = 15 000 − 12 000 = $3000.
(b) % loss = (3000/15 000) × 100 = 20% loss.
(c) Manager's 20% claim is correct. ✓
1.3 — Bakery wants 30% profit on $8 CP cakes
(a) SP = 8 × 1.30 = $10.40.
(b) Profit = 10.40 − 8 = $2.40 per cake.
(c) If SP = $11.20: profit = 11.20 − 8 = $3.20; % profit = (3.20/8) × 100 = 40% profit.
1.4 — Maya's phone $1500 → $450 trade-in
(a) Loss = 1500 − 450 = $1050.
(b) % loss = (1050/1500) × 100 = 70% loss.
(c) Recovered = (450/1500) × 100 = 30% of original cost — the other 70% was depreciation.
1.5 — Pen wholesaler $1.20 CP
(a) SP at 25% profit = 1.20 × 1.25 = $1.50 per pen.
(b) For 80 pens: revenue = 80 × 1.50 = $120; total CP = 80 × 1.20 = $96; total profit = 120 − 96 = $24 profit. (Or per-pen profit × 80 = 0.30 × 80 = $24.)
(c) SP at 50% profit = 1.20 × 1.50 = $1.80 per pen.
2.1 — Explain your thinking (sample response)
(i) Brand A: % profit = 15/30 × 100 = 50%. Brand B: % profit = 20/80 × 100 = 25%.
(ii) Brand A has the higher percentage profit per shirt — 50% vs 25%, double the rate.
(iii) A higher dollar profit doesn't always mean a better margin because the dollar profit is taken relative to the CP. Brand B does earn $20 per shirt vs Brand A's $15, but Brand B spends $80 to make that $20, while Brand A spends only $30 to make $15. So for every $1 Brand A invests, it gets 50 cents back as profit; Brand B only gets 25 cents back. % profit measures efficiency per dollar invested, while dollar profit just measures total cash. For investors deciding where to put money, the percentage matters more than the raw dollars.
Marking: 1 mark for Brand A's 50%; 1 mark for Brand B's 25%; 1 mark for clearly stating Brand A has higher % profit; 1 mark for a clear explanation that uses "% profit measures efficiency per dollar invested" or equivalent reasoning.