The number of dolls owned by Cheryl, Diana and Ella is in the ratio 6:3:2.

Question

If Ella has x dolls how many dolls do Cheryl and Diana have in terms of x?

Answer 1

Important rule:

  If numbers a, b, and c are in the ratio of d, e, and f, then there is an integer factor n such that:

       a=nd

       b=ne

       c=nf

 

This means that a/n reduces to d, that b/n reduces to e, and c/n reduces to f.

 

In this problem:   f=2 (ratio for Ella) and c=x (actual for Ella), so

              and c=nf=2n=x. therefore n=x/2

 

     a=nd=(x/2)6     so, a=3x

     b=ne=(x/2)3     so, b=(3/2)x

     c=nf=(x/2)2      so, c=x       [this was given; check!]

 

To double-check:

   Let x=4 (so, n=x/2=2) and the ratio is 6:3:2

    so,

     a=nd=2*6=12

     b=ne=2*3=6

     c=nf=2*2=4

   the actual values are: 12:6:4, which, when reduced, are 6:3:2

Answer 2

Diana has 3/2 times more than Ella and Cheryl has 6/2 = 3 times more.  So the answers would be 3x/2 and 3x respectively.