Divide 4864 into three parts such that the second part is 5 times of the first and the ratio of the second part to the third part is 3:4.

Question

Divide 4864 into three parts such that the second part is 5 times of the first and the ratio of the second part to the third part is 3:4.

Answer 1

Another way to look at it is that 1/5 of 3 is .6, so our ratio, though not in whole numbers, is .6:3:4, making 7.6 parts.

 

4864/7.6 = 640

 

.6(640) = 384

3(640) = 1920

4(640) = 2560

 

384:1920 = 1:5 and 1920:2560 = 3:4

Answer 2

Let:
   x = first part
   y = second part
   z = third part
 
The ratios are x:y:z
 
"second part is 5 times of the first"    means   y=5x
   So, now the three parts are x:5x:z
 
"ratio of the second part to the third part is 3:4"   means
        y/z=3/4
  
     So, z/y = 4/3             [invert]
           z = (4/3)y           [multiply both sides by y]
 
     But, y = 5x, so:
           z = (4/3)5x
           z = (20/3)x
 
Now, the ratio is:
        x : 5x : (20/3)x
        3x: 15x: 20x              [multiply by 3; this is 38 parts of size x]
 
       38x = 4864
          x = 128               [divide both sides by 38]
 
4864 is split as follows:    384 : 1920 : 2560
 
Check:
   Is 1920 = 5*384   ?
        1920 = 1920   ?yes
   Is 1920/2560 = 3/4   ?
        3/4 = 3/4   ?yes