Maths: Word Problems

A word problem tells a short story with some numbers in it. The question comes at the end, on the last line.

The sums are not the hard part. The plan is: which sums to do, in which order. Then you pick from five answers.

In GL's papers, a wrong answer is often a half-done plan: a number you reach part-way through, set out as an option. The video above and the worked example below work through the same question, with the options in the same order. The shorter one after it is the video's second question.

The method

Four steps: find what's asked; picture the story; plan, then finish every step; check it fits the story.

The picture in step 2 can be a bar: the whole is the full length, cut into the parts you know and the part that's missing.

Worked example

A party room costs £25 to hire, plus £5 for each child. A party costs £90 altogether. How many children went to the party?

A. 12 B. 13 C. 18 D. 23 E. 65

1. Find what's asked. Read the last line first. Here, it asks: how many children? So you're finding a number of children, not an amount of money.
2. Picture the story. The whole is the £90 the party costs altogether. One part is the £25 to hire the room. The rest is the children's money, £5 for each child, and that's the part that's missing. The hire is part of the £90. 18 is option C: all £90 shared into fives, with no hire. So C is out. 23 is option D: the hire added on top. But it's already inside the £90, so D is out.
3. Plan, then finish every step. First take the hire off: £90 − £25 = £65. 65 is option E, but that's only half-way: it's money, not children. So E is out. Then share the £65 into fives: £65 ÷ £5 = 13.
4. Check it fits the story. Put it back in: 13 fives are £65, and with the £25 hire, that's £90. The bar closes exactly. 12 is option A: 12 fives are £60, and with the hire that's £85, £5 short. So A is out. 13 is a whole number of children, and that's what was asked. So the answer is B.

Answer: B — 13 (£90 − £25 = £65 · £65 ÷ £5 = 13 children)

A second worked example: a shorter one

Amir buys some paints for £4.30 and a book for £6.50. He pays with a £20 note. How much change does he get?

A. £15.70 B. £13.50 C. £10.80 D. £9.20 E. £8.20

1. Find what's asked. The change he gets.
2. Picture the story. The £20 note is the whole. The paints and the book are two parts, and the change is the part that's missing.
3. Plan, then finish every step. Add, then take away. Add the two prices: £4.30 + £6.50 = £10.80. That's option C, but it's what he spent, only half-way, so C is out. Then take £10.80 from £20: £9.20.
4. Check it fits the story. Does the bar close? £4.30, £6.50 and £9.20 make £20 exactly. £15.70 leaves out the book, so A is out. £13.50 leaves out the paints, so B is out. £8.20 makes only £19, so E is out. So the answer is D.

Answer: D — £9.20 (£4.30 + £6.50 = £10.80 · £20 − £10.80 = £9.20)

Things to watch out for

1. Read the last line first. Know what you're finding before you start. Shop A sells 10 bread rolls for £5, and Shop B sells 2 for £1.70. The last line asks how much cheaper one roll is at Shop A than at Shop B. One roll costs 50p at Shop A and 85p at Shop B, but neither price is the difference. £3.30 compares whole packs. One roll is 35p cheaper.
2. Plan, then finish every step. A half-way answer can be one of the options. A school needs 100 chairs. It has 7 rows of 10, but 4 are broken. 7 tens are 70: that's option E. Take off the 4 broken ones: 66, option D. Only the last step, 100 − 66, gives 34.
3. Not every number is needed. And some need changing first. A farm has 514 sheep, and the question asks how many more lambs were born in March than in April. It only compares the lambs, so the 514 sheep aren't needed, but option D uses them. And in another question, 3.5 kg must become 3,500 g, because the question asks in grams.
4. Round to fit the story. Sometimes up, sometimes down. Lily saves £2.50 a week towards a board game that costs £22. 8 weeks make £20, not enough, so round up to 9 weeks. Rory has £2, and notebooks cost 55p. 3 cost £1.65, and a fourth won't fit, so round down to 3.

Related

• The complete 11+ question-type guide
• Maths: Ratio and Proportion — find what one part is worth, then scale
• Maths: Algebra — start from the end and flip every step
• Maths: Measures — spot the units and make them the same

All example questions come from the Brainblox question bank — practise this question type inside 25+ learning games, timed mock exams and focused practice. Brainblox is an independent app: not affiliated with, endorsed by or licensed by any exam board, school or assessment publisher, and it contains no past papers.