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Question

Three numbers are to one another 2:3:4. The sum of their cubes is 33957. Find the numbers.


Solution

Let the numbers be 2x, 3x and 4x
sum of cubes = 33957
⇒(2x)³ + (3x)³ + (4x)³ = 33957
⇒8x³ + 27x³ + 64x³ = 33957
⇒99x³ = 33957
⇒x³ = 33957/99 = 343
⇒x = ∛343 = 7

Numbers are:
2x = 2×7 = 14
3x = 3×7 = 21
4x = 4×7 = 28

 

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