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4024/22 Oct/Nov 2022, Question 5: Simultaneous Equations by Elimination

Cambridge O Level Mathematics 4024 · Paper 22 (Calculator) · Calculator · 11 marks

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The question, in short

A bag holds x five-cent and y ten-cent coins; form equations from coin count and total value, solve them, then work out machine output value and a bounds calculation for coin lines.

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

Part (ai) · 1 mark

Write an equation in x and y for the 130 coins in the bag.

  1. 1x + y = 130

Answerx + y = 130

Part (aii) · 1 mark

Write an equation in x and y for the $8.15 total value.

  1. 1Value in cents: 5x + 10y = 815

Answer5x + 10y = 815

Part (aiii) · 3 marks

Solve x + y = 130 and 5x + 10y = 815 simultaneously, showing working, to find how many of each coin.

  1. 15 × (x + y = 130): 5x + 5y = 650
  2. 2Subtract from 5x + 10y = 815: 5y = 165, y = 33
  3. 3x = 130 − 33 = 97
  4. 4Five-cent coins = 97, ten-cent coins = 33

AnswerFive-cent coins = 97, Ten-cent coins = 33

Part (b) · 3 marks

Find the dollar value of coins made in 300 days at 720 coins per minute, 24 hours daily, in standard form to 3 significant figures.

  1. 1Coins = 720 × 60 × 24 × 300 = 311 040 000
  2. 2Value = 311 040 000 × 0.05 = $15 552 000
  3. 3= 1.56 × 10⁷ dollars (3 s.f.)

Answer1.56 × 10⁷

Part (c) · 3 marks

Using diameters 21.2 mm and 17.9 mm to the nearest 0.1 mm, find the upper bound of the difference between 10-coin lines.

  1. 1Upper bound of five-cent diameter = 21.25 mm; lower bound of ten-cent diameter = 17.85 mm
  2. 2Upper bound of difference = 21.25 × 10 − 17.85 × 10
  3. 3= 212.5 − 178.5 = 34 mm

Answer34

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