Mathematics • Year 8 • Unit 1 • Lesson 9
Profit and Loss
Build fluency identifying CP (cost price) and SP (selling price), then computing profit (SP − CP when SP > CP) or loss (CP − SP when SP < CP). Both reported as positive dollar amounts, with the word telling direction.
1. I do — fully worked example
Read every line. This is a multiple-items profit problem — the kind a stall owner or shop owner solves every day.
Problem. You buy 12 books for $5 each and sell 10 of them at $8 each. The other 2 you lose (couldn't sell). What is the total profit or loss?
Step 1 — Total CP: cost of EVERYTHING you bought.
Total CP = 12 × 5 = $60
Reason: ALL 12 books cost you money, including the 2 that didn't sell. Unsold stock still counts as cost.
Step 2 — Total SP: revenue from items actually sold.
Total SP = 10 × 8 + 2 × 0 = $80
Reason: only the 10 sold give you money. The lost 2 give $0.
Step 3 — Compare: SP > CP?
$80 > $60? YES → PROFIT
Reason: you received more money than you spent. Profit-direction.
Step 4 — Compute the profit amount.
Profit = SP − CP = 80 − 60 = $20
Reason: profit is always a positive dollar amount; the word "profit" tells the direction.
Answer: $20 profit (even after losing 2 books).
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 market stall buys a tray of mangoes for $48 and sells the whole tray for $72. What is the profit or loss?
Step 1 — Identify CP and SP:
CP = $______ (what you PAID). SP = $______ (what you SOLD for).
Step 2 — Compare:
Is SP > CP? ______ → ______ (profit or loss).
Step 3 — Compute the amount:
Amount = ______ − ______ = $______
Step 4 — Write the final answer in words:
$______ ______ (profit / loss / break-even)
3. You do — independent practice
Show your working under each problem. The first four are foundation (single item, identify profit or loss). The middle two are standard (multiple items). The last two are extension (find CP or SP given the profit/loss).
Foundation — single item
3.1 CP $30, SP $45. State whether it's a profit or loss, and the amount. 1 mark
3.2 CP $120, SP $90. State whether it's a profit or loss, and the amount. 1 mark
3.3 CP $300, SP $300. State the outcome. 1 mark
3.4 A bike was bought for $300 and sold for $450. Find the profit (in dollars). 1 mark
Standard — multiple items
3.5 A trader buys 30 phones at $120 each and sells all 30 at $150 each. Find the total profit. 2 marks
3.6 Buy 5 books at $4 each, sell ALL of them at $6 each. Find the total profit. 2 marks
Extension — find CP or SP
3.7 You sell at $240 and make a $60 profit. What was the cost price? 2 marks
3.8 A baker buys flour for $50, makes 20 cakes, and sells 18 of them at $5 each (the other 2 burn). Find the total profit. 2 marks
How did this worksheet feel?
What I'll revisit before next class:
Section 2 — We do (mangoes $48 → $72)
Step 1: CP = $48; SP = $72.
Step 2: Is SP > CP? Yes → profit.
Step 3: Amount = 72 − 48 = $24.
Step 4: $24 profit.
3.1 — CP $30, SP $45
SP > CP, so PROFIT. Amount = 45 − 30 = $15 profit.
3.2 — CP $120, SP $90
SP < CP, so LOSS. Amount = 120 − 90 = $30 loss.
3.3 — CP $300, SP $300
SP = CP, so break-even (no profit, no loss).
3.4 — Bike $300 → $450
Profit = 450 − 300 = $150 profit.
3.5 — 30 phones, $120 CP → $150 SP
Total CP = 30 × 120 = $3600. Total SP = 30 × 150 = $4500. Profit = 4500 − 3600 = $900 profit.
3.6 — 5 books, $4 → $6
Total CP = 5 × 4 = $20. Total SP = 5 × 6 = $30. Profit = 30 − 20 = $10 profit.
3.7 — Sold at $240 with $60 profit
CP = SP − profit = 240 − 60 = $180.
3.8 — Baker, $50 flour, 18 of 20 cakes sold at $5
Total CP = $50 (the flour — all of it). Total SP = 18 × 5 + 2 × 0 = $90 + $0 = $90. Profit = 90 − 50 = $40 profit. (Even though 2 cakes burnt, the bake was still profitable.)