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The sum of cubes of two numbers is 280. If the numbers are in the ratio 2:3, find the smallest number.

Correct answer: A. 4

  • A. 4
  • B. 6
  • C. 3
  • D. 2

Explanation

Write the numbers as 2k and 3k. Their cubes give (2k)^3 + (3k)^3 = 8k^3 + 27k^3 = 35k^3 = 280, so k^3 = 8 and k = 2; the smaller number is 2k = 4. The likely mistake is choosing 6 by taking the larger ratio term instead of the smaller one.

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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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