Multi-Step Word Problems
Multi-step word problems require two or more arithmetic operations to reach the answer. They are the most common type of applied maths problem in real life.
Key Approach
- Read the entire problem before doing any calculation.
- Identify what you are asked to find.
- List the given facts.
- Plan the steps in order.
- Calculate one step at a time, showing your working.
- Answer with appropriate units.
- Check using estimation or inverse operations.
Worked Examples
Medium
A shop has 4 boxes of red pens (8 per box) and 3 boxes of blue pens (12 per box). How many pens in total?
Red: 4 × 8 = 32. Blue: 3 × 12 = 36. Total: 32 + 36 = 68 pens
Hard
A hall can seat 350 people. Tickets cost £12 for adults and £7 for children. 240 adults and 95 children attend. What is the total ticket revenue, and how many seats are empty?
Adult revenue: 240 × £12 = £2,880.
Child revenue: 95 × £7 = £665.
Total revenue: £2,880 + £665 = £3,545.
Empty seats: 350 − (240 + 95) = 350 − 335 = 15 empty seats
Key Takeaways
- Plan all steps before calculating.
- Label each step clearly with its meaning.
- Don't rush: one step at a time avoids compounding errors.
- Estimate the final answer before starting to check reasonableness.
Practice Questions
- A baker makes 144 biscuits. She packs them in boxes of 12 and sells each box for £3.50. How much does she earn if she sells all the boxes?
- A train has 8 carriages each holding 64 passengers. If 318 passengers are on board, how many empty seats are there?
- James earns £1,200 per month. He spends £450 on rent, £120 on food, and saves the rest. How much does he save in 6 months?
- A recipe uses 250 g of flour per cake. A bag holds 1.5 kg. How many complete cakes can be made and how many grams are left?
- Tickets for a theme park are £22 for adults and £14 for children. A family of 2 adults and 3 children buys tickets. What is the total cost? If they pay with a £100 note, how much change do they get?