Question

the sum of three cubes of three numbers which are in the ratio 1:2:3 is7776 find the numbers

Answer 1

Ratio of the 3 numbers = 1 : 2 : 3

Define x:

Let x be the constant ratio

Ratio of the 3 numbers = 1x : 2x : 3x

Solve x:

Given that the sum of their cubes is 7776

(1x)³ + (2x)³ + (3x)³ = 7776

1x³ + 8x³ + 27x³ = 7776

36x³ = 7776

x³ = 7776 ÷ 36

x³ = 216

x = ∛216

x = 6

Find the numbers:

x = 6

2x = 2(6) = 12

3x = 3(6) = 18

Answer: The numbers are 6, 12 and 18