Question

Three numbers are in the ratio 1:2:3. The sum of their cubes is 7776. Find the numbers.

Answer 1

Let the numbers be x, 2x and 3x

$\text{sum of their cubes is}{x}^3+8x^3+27x^3=7776$

$36x^3=7776$

$x^3=216$

$x=\sqrt[3]{36\times 6\times 6}$

$x=6$

$2x=2\left(6\right)=12$

$3x=3\left(6\right)=18$

The numbers are 6,12,18