SOLUTION: the ratio of the ages of A:B=6:5, AND THE AGE of each C and D is 9/10 times that Of B . Age of F is less than A but greater then B . The ratio of age of B&E is 2:3 ,also age of A i

Question 983538: the ratio of the ages of A:B=6:5, AND THE AGE of each C and D is 9/10 times that Of B . Age of F is less than A but greater then B . The ratio of age of B&E is 2:3 ,also age of A is 3 years less than E .What is the ratio of age of A and F ,if all the pages are in integers ?
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
= age of A,
= age of B,
= age of C,
= age of D,
= age of E, and
= age of F.
We can use the ratios to calculate , , , and in terms of :
The ratio of the ages of A:B=6:5. ---> -->--> .
The age of each C and D is 9/10 times that Of B. ---> .
The ratio of age of B&E is 2:3. ---> -->-->--> .
For all those ages to be integers, must be a multiple of and ,
so it must be a multiple of .
We can use "guess and check" from here, trying 12, 24, 36, etc as values for .
We can also say that for some whole number ,
and express everyone's age as a function of :
,
,
, and

The age of A is 3 years less than E. ---> -->-->-->--> .
So,
and .
Since the age of F is less than A but greater than B, ,
and the rati we need is
.
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