Question

three numbers are in the ratio 3:4:5 . The sum of their cubes is 27000 . Find the numbers.​

Answer 1

Answer:

Answer:

The three numbers are 15, 20, 25

Step-by-step explanation:

Given the three numbers which are in ratio 3:4:5 and their sum of cubes is 27000.

we have to find the numbers.

\text{Let the three numbers are 3x, 4x, 5x so that their ratio is 3:4:5}Let the three numbers are 3x, 4x, 5x so that their ratio is 3:4:5

As their sum of cubes is 27000  

(3x)^3+(4x)^3+(5x)^3=27000(3x)3+(4x)3+(5x)3=27000

27x^3+64x^3+125x^2=2700027x3+64x3+125x2=27000

216x^3=27000216x3=27000

x^3=\frac{27000}{216}=125x3=21627000=125

Taking cube root on both sides, we get

x=5x=5

3x=3\times 5=15, 4x=4\times 5=20, 5x=5\times 5=253x=3×5=15,4x=4×5=20,5x=5×5=25

Hence, the three numbers are 15, 20, 25