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0580/32 May/Jun 2026, Question 14: Constructing Equations

Cambridge IGCSE Mathematics 0580 · Paper 32 (Core) · Calculator · 7 marks

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The question, in short

A jar starts with 60 counters; Kan adds C and Mo adds 2C + 7. Form a simplified total, then split it equally and use a given share to find C.

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Part (a) · 2 marks

Combine the starting 60 with C and 2C + 7 to give the jar's new total in simplest form.

  1. 160 + C + 2C + 7
  2. 2= 3C + 67

Answer3C + 67

Part (bi) · 1 mark

Express how many counters each person gets when the total is split into two equal shares.

  1. 1Total counters = 60 + C + (2C + 7) = 3C + 67
  2. 2Share equally between 2 people: each receives (3C + 67)/2

Answer(3C + 67)/2

Part (bii) · 4 marks

Given that each share equals 86, solve for the value of C.

  1. 1Total counters = 60 + C + (2C + 7) = 3C + 67
  2. 2Each gets half the total: (3C + 67)/2 = 86
  3. 3Multiply by 2: 3C + 67 = 172
  4. 43C = 172 − 67 = 105, so C = 35

Answer35

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Also searched as: 0580/32/M/J/26 · 0580_s26_qp_32 · 0580 s26 32 · question 14.
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