Break-even & margin
Profit = revenue − costs. Break-even units = fixed costs ÷ (price − variable cost). Round up: you can’t sell part of an item.
Markup divides the profit by the cost; margin divides it by the price. Alberta has 5% GST and no PST. Every business here is made up.
One step
Profit, cost and percent.Card stall
You sell 30 handmade cards at $4. Each costs $1.50 to make, and the table costs $25. What is the profit?
Total cost
Fixed costs are $35; each item costs $2. What is the total cost for 40 items, and the average cost per item?
Two percents
An item costs $6 and sells for $9. Find the markup and the margin, as percents.
Growth
A tutoring service grew from 40 to 50 customers. What is the growth percent?
Two or three steps
Write the formula, then fill it in.Break-even
A bake-sale table costs $72. Cookie boxes sell for $12 and cost $4 to make. How many boxes to break even? Which box is the first to make a profit?
Price it
A bookmark costs $2 to make. Find the price for a 60% margin, and the price for a 60% markup. Which is higher, and why?
Borrowing
Borrow $600 at 8% a year for 2 years. Find the simple interest, then the compound interest (interest on interest).
One customer
Music lessons sell for $20 and cost $2 in materials. $45 of posters brings 3 students, who each book 6 lessons. Find the contribution, CAC and LTV.
The sale
An item sells for $10 and costs $4. In a 20% off sale, what is the new price? By what percent does the profit per item fall?
GST
A registered seller adds 5% GST to a $24 price. What does the customer pay?
Equations
Profit lines and curves (pp.17–18).Profit goal
Profit P = 6q − 90. Find the break-even q, then the q that makes a $120 profit.
Two tables
Plan A costs a flat $45. Plan B costs $15 plus $1.50 per item sold. When do they cost the same?
Best price
At price p you sell 80 − 10p items. Each costs $2, plus $40 fixed: P = (p − 2)(80 − 10p) − 40. Find P at $4, $5 and $6. Which is best?
Zero profit
Set P = 0 and simplify to p² − 10p + 20 = 0. Use the quadratic formula. What do the two prices mean?
Your turn to be the founder
- Invent a tiny business: a stall, a service, a craft.
- List its price, its variable cost and its fixed costs.
- Find its break-even point and its margin. Would you start it?
My problem, and my worked answer:
Try every problem first, then check here. Wrong answers are useful: find the step where your work and the key split apart.
The key never prints with Print my work or Print blank. Open it to get its own Print the answer key button.
Answer key
Worked solutions. Businesses and prices are fictional; tax rules checked October 2026 (book p.11).