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0580/11 May/Jun 2023, Question 25: Simultaneous Equations by Elimination

Cambridge IGCSE Mathematics 0580 · Paper 11 (Core) · Calculator · 5 marks

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The question, in short

Adult tickets cost $a and child tickets $c at a cinema; form equations from two purchases and solve the simultaneous equations for a and c, showing working.

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

Part (a) · 1 mark

Farah buys 3 adult and 4 child tickets for $38.50; fill in the missing right-hand side of 3a + 4c = ...

  1. 13a + 4c = 38.5

Answer38.5

Part (b) · 1 mark

Hana buys 6 adult and 5 child tickets for $65.00; give a second equation linking a and c.

  1. 16 adult tickets cost 6a and 5 child tickets cost 5c
  2. 26a + 5c = 65

Answer6a + 5c = 65

Part (c) · 3 marks

Using 3a + 4c = 38.5 and 6a + 5c = 65, work out the values of a and c, showing every step.

  1. 13a + 4c = 38.5 → × 2: 6a + 8c = 77
  2. 2(6a + 8c) − (6a + 5c) = 77 − 65
  3. 33c = 12, so c = 4
  4. 43a + 4 × 4 = 38.5, so 3a = 22.5
  5. 5a = 7.5, c = 4

Answera = 7.5, c = 4

Stuck on a step? Read the free lesson: Simultaneous Equations by Elimination

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Also searched as: 0580/11/M/J/23 · 0580_s23_qp_11 · 0580 s23 11 · question 25.
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