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4024/21 May/Jun 2024, Question 5: Dividing in a Given Ratio

Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 7 marks

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The question, in short

Solve three problems: equate two companies' box-moving charges, bound the number of 4 kg boxes a 770 kg van can carry, and use two ratios with 72 large boxes to find total boxes.

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

Part (a) · 2 marks

Find how many boxes make Company A's cost (0.50 per box plus 125) equal Company B's fixed 350.

  1. 10.5x + 125 = 350
  2. 20.5x = 225, so x = 450 boxes

Answer450

Part (b) · 2 marks

With box mass 4 kg to nearest kg and van limit 770 kg, find the upper bound on boxes carried.

  1. 1Most boxes fit when each box is as light as it could be.
  2. 24 kg to the nearest kg has lower bound 3.5 kg
  3. 3770 ÷ 3.5 = 220

Answer220

Part (c) · 3 marks

Given S:M = 2:7, S:L = 5:4 and 72 L boxes, find the total number of boxes.

  1. 1S : M = 2 : 7 = 10 : 35 and S : L = 5 : 4 = 10 : 8
  2. 2S : M : L = 10 : 35 : 8; L = 8k = 72 so k = 9
  3. 3S = 90, M = 315, L = 72
  4. 4Total = 90 + 315 + 72 = 477

Answer477

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