What is important to know about Forming equations from context?

Choose a letter to represent the unknown and state what it stands for.

What is important to know about Forming equations from context?

Translate words into algebra: "more than" = +, "times" = ×, "is" = =.

What is important to know about Forming equations from context?

Use the context to set up an equation, then solve it.

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Algebra · Foundation & Higher

Forming equations from context

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.

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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