Mathematics • Year 8 • Unit 1 • Lesson 9
Profit and Loss — Mixed Challenge
Pull together everything from Lesson 9: single-item profit/loss, multi-item totals, break-even, finding CP from SP and profit, and accounting for unsold stock. Six mixed problems, one "find the mistake" on swapped CP and SP, and one open-ended business challenge.
1. Mixed problems — choose the right move
Each question uses a different combination of ideas from Lesson 9. Decide whether you have a single item or multiple items, and whether you are finding profit, CP, or SP before you start writing. Show your working. 3 marks each
1.1 CP $540, SP $690. Profit or loss? State the amount.
1.2 CP $1250, SP $950. Profit or loss? State the amount.
1.3 A jacket cost $80 and sold for $65. Outcome and amount?
1.4 You sell at $400 and make a $50 loss. What was the cost price?
1.5 A baker buys flour for $50, makes 20 cakes, and sells 18 at $5 each. What is the total profit? (The other 2 cakes are unsold and given away.)
1.6 A trader buys 50 hats at $12 each and sells all 50 at $20 each. Find the total profit.
2. Find the mistake
A Year 8 student tried to find the profit or loss when buying a phone for $200 and selling it for $175. Their working is shown below. Exactly one line contains a mistake. Spot it, explain why it's wrong, then re-do the working correctly. 3 marks
Student's working — Bought phone $200, sold $175:
Line 1: I paid $200 and got $175 back, so CP = $175 and SP = $200.
Line 2: SP > CP ($200 > $175), so it's a profit.
Line 3: Profit = SP − CP = 200 − 175 = $25.
Line 4: Final answer: $25 profit.
(a) Which line contains the mistake?
(b) Explain in one or two sentences why that line is wrong.
(c) Write out the corrected working in full, including the corrected outcome.
Stuck? "Bought for $200" means CP = $200 (what you PAID). "Sold for $175" means SP = $175 (what you RECEIVED). The student swapped them.3. Open-ended challenge — design a stall
This question has more than one valid answer. 4 marks
3.1 You are running a stall at the school fete. You have $100 of cash to spend on stock. Your goal is to make at least $80 profit after the day is done.
Design a stall plan that includes:
(i) ONE product you would sell (e.g. cupcakes, slushies, friendship bracelets).
(ii) The CP per unit and how many units you can afford with $100.
(iii) The SP per unit you would charge.
(iv) A REALISTIC assumption about how many units you'd actually sell on the day (don't assume 100%).
(v) The total profit you'd make under that assumption — show that it meets the $80 target.
Bonus: Briefly say what would happen to your profit if your sell-through rate dropped by 25% (e.g. weather, low fete turnout).
How did this worksheet feel?
What I'll revisit before next class:
1.1 — CP $540, SP $690
SP > CP. Profit = 690 − 540 = $150 profit.
1.2 — CP $1250, SP $950
SP < CP. Loss = 1250 − 950 = $300 loss.
1.3 — Jacket $80 → $65
SP < CP. Loss = 80 − 65 = $15 loss.
1.4 — Sold $400 with $50 loss
CP = SP + loss = 400 + 50 = $450.
1.5 — Baker, $50 flour, 18 of 20 cakes sold at $5
Total CP = $50. Total SP = 18 × 5 + 2 × 0 = $90. Profit = 90 − 50 = $40 profit.
1.6 — 50 hats $12 → $20 each
Total CP = 50 × 12 = $600. Total SP = 50 × 20 = $1000. Profit = 1000 − 600 = $400 profit.
2 — Find the mistake
(a) The mistake is on Line 1 (the wrong CP and SP are then carried into Lines 2 and 3).
(b) The student swapped CP and SP. "I paid $200" means CP = $200 (the cost price is what you PAID). "Got $175 back" means SP = $175 (the selling price is what you RECEIVED). Once swapped, the rest of the working concludes a profit instead of a loss.
(c) Corrected working:
CP = $200 (paid). SP = $175 (received).
SP < CP, so it's a LOSS.
Loss = CP − SP = 200 − 175 = $25 loss.
3 — Open-ended challenge (sample plan)
Sample plan — slushie stall:
(i) Product: slushies.
(ii) CP per slushie = $1.25 (cup + syrup + ice cost). $100 buys 80 slushies.
(iii) SP per slushie = $4.
(iv) Realistic assumption: hot day, sell 75 of 80 (95% sell-through).
(v) Total CP = $100. Total SP = 75 × $4 = $300. Profit = 300 − 100 = $200 profit — well above the $80 target. ✓
Bonus — sell-through drops 25%: 75 × 0.75 ≈ 56 slushies sold. Total SP = 56 × $4 = $224. Profit = 224 − 100 = $124 profit — still well above $80 but cut by $76. Conclusion: the slushie plan is robust to weather/low turnout.
Other valid plans:
• Cupcakes at CP $2.50, SP $5, 40 units bought, 30 sold: Profit = 30 × 5 − 100 = $50 → BELOW target. Needs higher SP or better sell-through.
• Friendship bracelets at CP $0.80, SP $3, 125 units bought, 80 sold: Profit = 80 × 3 − 100 = $140 → above target.
Marking: 1 mark for choosing a product with realistic CP that fits $100 stock budget; 1 mark for showing total CP, total SP, and total profit calculation; 1 mark for a sensible "realistic" sell-through assumption (not 100%); 1 mark for confirming the $80 target is met AND completing the bonus drop-25% analysis. Multiple valid plans possible — markers verify arithmetic only.