Multi-Step Word Problems

Multi-step word problems are at the heart of the SET 11+ mathematics papers. The Sutton Selective Eligibility Test (SET) is a two-stage exam used to select students for grammar schools in the London Borough of Sutton. Stage 1 is a multiple-choice paper, but Stage 2 is a written paper where you must show your working clearly. This lesson will teach you a reliable method for breaking down and solving any multi-step problem — the kind of question that appears heavily on both stages.

Why Multi-Step Problems Matter on the SET

The SET maths papers are designed to test your reasoning as well as your number skills. Many questions look simple at first glance, but they contain two, three, or even four steps before you reach the answer. On Stage 2, marks are awarded for your working as well as your final answer, so you must write every step clearly.

The RICE Method

Use this four-step approach for every word problem:

Step	Letter	What to do
1	R — Read	Read the entire question carefully. Read it a second time.
2	I — Identify	Identify the key numbers and what the question is asking. Underline them.
3	C — Calculate	Carry out the calculations step by step. Write each step clearly.
4	E — Evaluate	Check your answer. Does it make sense in the context of the question?

Top Tip: On the SET Stage 2 paper, the final answer is not always the last number you calculate. Always re-read the question before writing your answer.

Key Words That Signal Operations

Recognising key words in a problem helps you decide which operation to use at each step.

Key words	Operation
total, altogether, sum, combined, increase	Addition
difference, fewer, less than, reduce, remain, left	Subtraction
times, product, each, every, groups of, per	Multiplication
share, split, divide, per (sharing context), equally	Division
of (with fractions or percentages)	Multiplication

Watch out: "How many more" means you need to subtract, not add!

Worked Example 1: Shopping Problem

Emma buys 4 books at £3.75 each and 3 pens at £1.20 each. She pays with a £20 note. How much change does she receive?

Step 1 (Read): We need the total cost first, then the change from £20.

Step 2 (Identify): 4 books at £3.75, 3 pens at £1.20, paid with £20.

Step 3 (Calculate):

Cost of books: 4 × £3.75 = £15.00
Cost of pens: 3 × £1.20 = £3.60
Total cost: £15.00 + £3.60 = £18.60
Change: £20.00 - £18.60 = £1.40

Step 4 (Evaluate): £1.40 is reasonable — the items cost just over £18, so change from £20 should be just under £2. Correct!

Worked Example 2: Distance, Speed, and Time

A cyclist travels at 15 km per hour. She sets off at 10:20 and arrives at 12:00. How far does she cycle?

Step 1: Find the time taken, then use it to calculate the distance.

Step 2: Speed = 15 km/h. Departure = 10:20. Arrival = 12:00.

Step 3:

Time taken: from 10:20 to 12:00 = 1 hour 40 minutes = 1 and 2/3 hours = 5/3 hours
Distance = speed × time = 15 × 5/3 = 25 km

Step 4: 25 km in 1 hour 40 minutes at 15 km/h — that checks out.

Worked Example 3: Fractions in a Real Situation

A baker makes 360 biscuits. He sells 2/5 of them in the morning. In the afternoon, he sells 1/3 of the remaining biscuits. How many biscuits does he have left?

Step 1: This is a three-step problem involving fractions.

Step 2: 360 biscuits, sells 2/5, then sells 1/3 of the remainder.

Step 3:

Morning sales: 2/5 × 360 = 144 biscuits sold
Remaining after morning: 360 - 144 = 216 biscuits
Afternoon sales: 1/3 × 216 = 72 biscuits sold
Remaining: 216 - 72 = 144 biscuits

Step 4: 144 + 72 + 144 = 360. All biscuits accounted for. Correct!

Worked Example 4: Interpreting Remainders

A school needs to transport 170 children on a trip. Each minibus holds 24 children. How many minibuses are needed?

Step 1: Divide and think about what the remainder means.

Step 2: 170 children, 24 per minibus.

Step 3:

170 ÷ 24 = 7 remainder 2
You cannot leave 2 children behind!
8 minibuses are needed.

Step 4: 7 minibuses hold 168 children, leaving 2 who need an eighth minibus. The answer is 8, not 7.

SET Tip: Both stages of the SET love remainder questions. Always ask yourself: do I round up or down in this real-life situation?

Worked Example 5: Percentage and Profit

A trader buys 60 candles at 45p each. She sells them in boxes of 5 for £3.50. She sells all the candles. What is her total profit?

Step 1: Find the total cost, total income, then subtract.

Step 2: 60 candles at 45p each. Sells in boxes of 5 for £3.50.

Step 3:

Total cost: 60 × £0.45 = £27.00
Number of boxes: 60 ÷ 5 = 12 boxes
Total income: 12 × £3.50 = £42.00
Profit: £42.00 - £27.00 = £15.00

Common Mistakes to Avoid

Mistake	How to avoid it
Answering the wrong question	Re-read the final sentence before writing your answer
Forgetting a step	Write every calculation down, even simple ones
Mixing up units (e.g. pence and pounds)	Convert everything to the same unit at the start
Rounding at the wrong stage	Only round at the very end, if at all
Ignoring remainders	Think about the real-life meaning of the remainder

Practice Problems

A box of 8 muffins costs £5.60. A single muffin costs 85p. Which is cheaper per muffin — the box or buying individually? How much do you save per muffin?
A train leaves London at 13:45 and arrives in Sutton at 14:22. The return train takes 8 minutes longer. What time does the return train arrive back in London if it departs Sutton at 16:30?
Mrs Khan earns £2,800 per month. She spends 1/4 on rent, 1/5 on food, and saves the rest. How much does she save each month?

Answers:

Box price per muffin: £5.60 ÷ 8 = 70p. Individual: 85p. Box is cheaper. Saving per muffin: 85p - 70p = 15p.
Outward journey: 14:22 - 13:45 = 37 minutes. Return journey: 37 + 8 = 45 minutes. Departure 16:30 + 45 minutes = 17:15.
Rent: 1/4 × £2,800 = £700. Food: 1/5 × £2,800 = £560. Spent: £700 + £560 = £1,260. Saved: £2,800 - £1,260 = £1,540.

Summary

Multi-step word problems are one of the most important question types on the SET 11+ maths papers. Use the RICE method every time: Read, Identify, Calculate, Evaluate. Break each problem into small, manageable steps, write your working clearly (especially on Stage 2), and always check that your final answer makes sense in the context of the question. With regular practice, you will become faster and more confident at these problems.