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4024/12 May/Jun 2024, Question 9: Constructing Equations

Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 4 marks

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The question, in short

A box holds red, blue and black pens: x red, blue exceeding red by 5, black double the blue. Form a simplified expression for the total, then use a total of 27 to find the red count.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (a) · 2 marks

Using x for the red pens, build and simplify an expression for how many pens the box holds altogether.

  1. 1Blue = x + 5, black = 2(x + 5) = 2x + 10
  2. 2Total = x + x + 5 + 2x + 10 = 4x + 15

Answer4x + 15

Part (b) · 2 marks

Given that the box contains 27 pens in total, work out how many of them are red.

  1. 14x + 15 = 27
  2. 24x = 12, so x = 3 red pens

Answer3

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