NavGanitMateby NavGreen Compute, AustraliaBased on Australian Curriculum: Mathematics v9.0
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Ratio and rate modelling

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A traditional Aboriginal method of making rope involves combining two types of fibres in a ratio of 4:5 (fibre X to fibre Y). If the total mass of the rope is 33 kg, what is the exact mass, in kilograms, of fibre X used?

Express your answer as a fraction or whole number.

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Worked solution

  1. The ratio of fibre X to fibre Y is 4:5, meaning for every 4 parts of fibre X, there are 5 parts of fibre Y.
  2. The total number of parts in the ratio is 4 + 5 = 9 parts.
  3. The total mass of the rope is 33 kg, which corresponds to 9 parts.
  4. To find the mass of one part, divide the total mass by the total number of parts: 33 kg ÷ 9 = 3.666... kg per part.
  5. Since fibre X makes up 4 parts, multiply the mass per part by 4: 4 × (33 ÷ 9) kg.
  6. Simplify the expression: 4 × 33 / 9 = 132 / 9.
  7. Simplify the fraction 132 / 9 by dividing numerator and denominator by their greatest common divisor, which is 3: 132 ÷ 3 = 44, 9 ÷ 3 = 3.
  8. The simplified fraction is 44 / 3.
  9. Convert 44 / 3 to a mixed number: 14 and 2/3 kg.
  10. The mass of fibre X is exactly 44/3 kg, which is approximately 14.67 kg, but the exact value is required.
  11. Check: 44/3 kg of fibre X and (5/9 × 33) = 165/9 = 55/3 kg of fibre Y. Total = 44/3 + 55/3 = 99/3 = 33 kg. The total matches.
  12. Therefore, the exact mass of fibre X used is 44/3 kg.

Reference answer: 44/3 kg

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