Forming equations involves translating a real-life situation into algebra, then solving the equation to find an unknown value. You must clearly define your variable.
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Revising forming equations from context the night before an exam? These are condensed revision notes — the facts, formulas and mistakes examiners actually mark, with no long explanations. Prefer a full walkthrough with step-by-step reasoning instead? Search “Forming equations from context GCSE” on the site for the complete guide.
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Key facts to remember
1Choose a letter to represent the unknown and state what it stands for.
2Translate words into algebra: "more than" = +, "times" = ×, "is" = =.
3Use the context to set up an equation, then solve it.
4Check your answer makes sense in the original context.
5Angles on a line, perimeters and ages are common contexts in GCSE questions.
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Worked examples
Example 1
The angles of a triangle are x°, (2x + 10)° and (x − 20)°. Find x.
Working
Angles in a triangle sum to 180°
x + (2x + 10) + (x − 20) = 180
4x − 10 = 180
4x = 190
x = 47.5
Answerx = 47.5°
Example 2
Sam is 3 times as old as Tom. In 5 years, their ages will sum to 46. Find their current ages.
Working
Let Tom's age = t, so Sam's age = 3t
In 5 years: (t + 5) + (3t + 5) = 46
4t + 10 = 46
4t = 36
t = 9, so Tom is 9 and Sam is 27
AnswerTom is 9, Sam is 27
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Common mistakes
✗Setting up the equation incorrectly by misreading the context.
✗Not defining the variable — writing equations without stating what x represents.
✗Forgetting to check the answer fits the original problem (e.g. negative age).
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Exam tips
✓Always write "Let x = …" before forming your equation.
✓After solving, substitute back into the original context to verify your answer.
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