Question

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

Answer 1

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.

{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

27x^3+64x^3+125x^2=27000

216x^3=27000

x^3=27000/216=125

Taking cube root on both sides, we get

x=5

3x=3×5=15, 4x=4× 5=20, 5x=5×5=25

Hence, the three numbers are 15, 20, 25

Answer 2

Answer:

Step-by-step explanation:

Let the numbers be 3x, 4x, 5x,

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

27x^3 + 64x^3 + 125x^3 = 27000,

216x^3 = 27000,

x^3 = 27000 / 216,

x^3 = (30 / 6) ^3,

⇒ x = 30 / 6,

⇒x=5.

So, the nos. are :-

1) 3x = 3*5 = 15,

2) 4x = 4*5 = 20,

3) 5x = 5*5 = 25,

Verification:

15³+20³+25³,

3375+8000+15625,

27000.

Hope it helps.