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X, Y and Z are quantities of the same kind such that X:Y=5:8 and Y:Z=4:7. Find X:Z.

Correct answer: C. 5:14

  • A. 32:35
  • B. 67:56
  • C. 5:14
  • D. 5:7

Explanation

Make the two expressions for Y equal: X:Y = 5:8 and Y:Z = 4:7, so multiply the second ratio by 2 to get Y:Z = 8:14. Thus X:Y:Z = 5:8:14 and X:Z = 5:14. The likely mistake is option d, 5:7, from failing to adjust the two different values assigned to Y.

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Ratios compare quantities in the same units, while proportions state that two ratios are equal. Problems cover simplification, division in a given ratio, direct and inverse variation, scale, and missing terms, with attention to the difference between a ratio and a fraction representing part of a whole.

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