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Three numbers are in the ratio 2:3:4. The sum of their cubes is 33957. Find the numbers.

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Three numbers are in the ratio 2:3:4. The sum of their cubes is 33957. Find the numbers.

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Let the numbers be 2x, 3x and 4x

(2x)3 + (3x)3 + (4x)3 = 33957

8x3 + 27x3 + 64x3 = 33957

99x3 = 33957

x3 = 33957/99

x3 = 343

x3 = 7 × 7 × 7

x3 = 73

x = 7

∴ The numbers are 2x = 2 × 7 = 14

3x = 3 × 7 = 21

4x = 4 × 7 = 28

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