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0580/32 Oct/Nov 2022, Question 5: Constructing Equations

Cambridge IGCSE Mathematics 0580 · Paper 32 (Core) · Calculator · 10 marks

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The question, in short

Three-part algebra question: form a cost expression, use ages to find three people's ages, and solve two simultaneous equations showing working.

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Part (a) · 2 marks

Write an expression in a and b for buying 6 kg of apples at a dollars per kg and 8 kg of bananas at b dollars per kg.

  1. 16 × a + 8 × b = 6a + 8b

Answer6a + 8b or 2(3a + 4b)

Part (b) · 4 marks

Cara is one more than double Asher's age; Brice is 22 older than Asher; ages total 167. Find each age.

  1. 1Asher a, Cara 2a + 1, Brice a + 22
  2. 2a + 2a + 1 + a + 22 = 167
  3. 34a + 23 = 167, so 4a = 144, a = 36
  4. 4Brice = 36 + 22 = 58, Cara = 2 × 36 + 1 = 73
  5. 5Asher 36, Brice 58, Cara 73

AnswerAsher 36, Brice 58, Cara 73

Part (c) · 4 marks

Solve 3x + 2y = 21 and 2x − 5y = 33 simultaneously, showing all steps.

  1. 1×2: 6x + 4y = 42; ×3: 6x − 15y = 99
  2. 2Subtract: 19y = −57, so y = −3
  3. 33x + 2(−3) = 21, so 3x = 27
  4. 4x = 9, y = −3

Answerx = 9, y = −3

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Also searched as: 0580/32/O/N/22 · 0580_w22_qp_32 · 0580 w22 32 · question 5.
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