Question

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

Answer 1

Answer:

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 = 3√343 = 7

Numbers are:

2x = 2 7 = 14

3x = 3 7 = 21

4x = 4 7 = 28