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0580/33 May/Jun 2025, Question 15: Constructing Equations

Cambridge IGCSE Mathematics 0580 · Paper 33 (Core) · Calculator · 7 marks

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The question, in short

Using the hire-cost table, calculate a total for two road bikes over three days, derive an electric-bike formula, and solve for equal-cost days.

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

Part (a) · 2 marks

Find the total charge for hiring 2 road bikes for 3 days using the table rates.

  1. 11 road bike for 3 days = 25 + 2 × 20 = 65
  2. 22 bikes = 2 × 65 = $130

Answer130

Part (bi) · 2 marks

Give a formula for E, the electric bike hire cost for d days, matching the given mountain bike form.

  1. 1The first day costs $70; the other d − 1 days cost $50 each.
  2. 2E = 70 + 50(d − 1)
  3. 3E = 70 + 50d − 50
  4. 4E = 50d + 20

Answer50d + 20

Part (bii) · 3 marks

Given an electric bike hired 6 days costs the same as a mountain bike for d days, determine d.

  1. 1Electric for 6 days: 70 + 5 × 50 = 320
  2. 2Set equal: 35d + 5 = 320
  3. 335d = 320 − 5 = 315
  4. 4d = 315 ÷ 35 = 9

Answer9

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