Question

If three numbers are in the ratio 3 : 4 : 5 such that the sum of their cubes is 1728, then the cube of the middle number is

Answer 1

Hi ,

Let a , b , c are three numbers ,

a : b : c = 3 : 4 : 5

Let a = 3x ,

b = 4x ,

c = 5x

according to the problem given ,

( 3x )³ + ( 4x )³ + ( 5x )³ = 1728

27x³ + 64x³ + 125x³ = 1728

216x³ = 1728

x³ = 1728/216

x³ = 8

x = 2

Therefore ,

cube of the middle number = b ³

= ( 4x )³

= ( 4 × 2 )³

= 8³

= 512

I hope this helps you.

: )

Answer 2

Hey there!

Ratio of numbers = 3 : 4 : 5

Let the numbers 3a , 4a , 5a.

According to question :

( 3a )³ + ( 4a )³ + ( 5a )³ = 1728

a³ ( 3³ + 4³ + 5³ ) = 1728

a³ = 1728 / ( 3³ + 4³ + 5³ )

a³ = 1728/216

a³ = 8

a = 2 .

The numbers 3(2) , 4(2) , 5(2) .

The numbers are 6 , 8 , 10

Cube of middle number

= 8³

= 512 .

Hope helped!