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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.

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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

  1. Angles in a triangle sum to 180°
  2. x + (2x + 10) + (x − 20) = 180
  3. 4x − 10 = 180
  4. 4x = 190
  5. 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

  1. Let Tom's age = t, so Sam's age = 3t
  2. In 5 years: (t + 5) + (3t + 5) = 46
  3. 4t + 10 = 46
  4. 4t = 36
  5. 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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