Question

three numbers are in the ratio 1 is to 2 is to 3 the sum of the Year cubes is 7776 find the number

Answer 1

Let the numbers be x, 2x and 3x.
x^3 + (2x)^3 + (3x)^3 = 7776.
(1 + 8 + 27)x^3 = 7776.
x^3 = 7776/36 = 3888/18 = 1944/9 = 216
x = 6
The numbers are 6, 12, 18.

Answer 2

let the numbers be x 2x 3x
x^3+(2x)^3+(3x)^3=7776
x^3(1+8+27)=7776
x^3 * 36=7776
x^3=7776/36=216
x= cube root of (216)
x=cube root of(2*2*2*3*3*3)
x=2*3=6
the numbers are 6,12,18