NavGanitMateby NavGreen Compute, AustraliaBased on Australian Curriculum: Mathematics v9.0
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A chemist prepares a solution by mixing two liquids in the ratio 5:7. If the total volume of the solution is 360 millilitres, how many millilitres of the first liquid are used?

Express your answer as an exact fraction.

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Explanation

Worked solution and answer (click to reveal)

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Worked solution

  1. The ratio of the two liquids is 5:7, meaning for every 5 parts of the first liquid, there are 7 parts of the second liquid.
  2. The total number of parts in the ratio is 5 + 7 = 12 parts.
  3. The total volume of the solution is 360 millilitres, which corresponds to 12 parts.
  4. To find the volume of one part, divide the total volume by the total number of parts: 360 mL ÷ 12 = 30 mL per part.
  5. The first liquid corresponds to 5 parts, so its volume is 5 × 30 mL = 150 mL.
  6. Express 150 mL as a fraction of the total volume: 150/360.
  7. Simplify the fraction 150/360 by dividing both numerator and denominator by their greatest common divisor, which is 30: 150 ÷ 30 = 5, 360 ÷ 30 = 12.
  8. The simplified fraction is 5/12.
  9. Since the question asks for the volume of the first liquid as an exact fraction of the total, and 5/12 of 360 mL is 150 mL, the answer is 5/12 of the total volume.
  10. Check: 5/12 × 360 = (5 × 360) / 12 = 1800 / 12 = 150 mL. This matches the earlier result.
  11. The volume of the first liquid is 150 millilitres, which is exactly 5/12 of the total solution.
  12. The final answer is expressed as the exact fraction 5/12 of the total volume.

Reference answer: 5/12

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