GCSE-readyForming and solving equations from words and diagrams
Many problems are equations in disguise. Choose a letter, write what you know as algebra, then solve.
Write the equation
2. Write each quantity in terms of that letter.
3. Use the fact in the question to make an equation.
Triangle angles x, 2x and x + 20: x + 2x + x + 20 = 180, so 4x = 160 and x = 40.
Two unknowns
3a + 2c = 34 and 2a + 4c = 36
Double the first: 6a + 4c = 68. Subtract the second: 4a = 32, so a = 8 and c = 5.
Answer the question asked
If the question asks for the largest angle or the cost of 5 tickets, finish the job.
Lengths and numbers of people cannot be negative.
A rectangle has length (2x + 3) cm and width x cm. Its perimeter is 36 cm. Find x.
- 2(2x + 3) + 2x = 36
- 4x + 6 + 2x = 36, so 6x = 30
- x = 5
Answer: x = 5
Define a letter, write each quantity with it, form an equation from the facts, solve, then answer the actual question.
- Not “2(n + 7) = 31”. That adds 7 before doubling.
Try two quick questions
See if it has sunk in. Answers are marked straight away.
2 more questions
Try each one, then tap to check.
A rectangle has length (4x + 6) cm and width x cm. Its perimeter is 52 cm. Find x.
Show the answer
Answer: 4
10x + 12 = 52, so x = 4.
Dad is five times as old as Lily. Their ages add up to 90. How old is Dad?
Show the answer
Answer: 75
x + 5x = 90, so x = 15 and Dad is 75.
Check you have got it
Answer 6 quick questions with instant marking. If you get one wrong, GCSE-ready shows you why and gives you another go. It is free, and you do not need an account.
- Pearson Edexcel GCSE Mathematics (1MA1) specification, topic A17, A19, A21
- Pearson Edexcel International GCSE Mathematics (4MA1) specification, topic 2.3, 2.4, 2.6
Checked by the GCSE-ready editorial team, 17 October 2026. Last updated 2 October 2026. Spotted a mistake? Tell us and we will fix it.