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

Explanation

Let the numbers be `2x, 3x` and `4x`
Sum of cubes `= 33957`
`⇒(2x)^3+ (3x)^3 + (4x)^3= 33957`
`⇒8x^3+ 27x^3+ 64x^3 = 33957`
`⇒99x^3 = 33957`
`⇒x^3= 33957/99 = 343`
`⇒x = root(3)(343) = 7`
Numbers are:
`2x = 2 xx 7 = 14`
`3x = 3 xx 7 = 21`
`4x = 4 xx 7 = 28`