Problema Solution

whe joe was half as old as kate,his cousin jean was thirty-eight. when kate was half as old as jean.then joe himself was seventeen. their ages total one one three so what must those three ages be?

Answer provided by our tutors

Let:

a = joe's age

b = kate's age

c = jean's age


Equation for their current ages:

a+b+c=113


Some t years ago, Jean was 38, Joe was 'a' and Kate was 'b' years old:

(a+t) + (b+t) + (38 + t) = 113

and Joe was half as old as Kate at that time, or b=2a, so:

a + t + 2a +2t =113-38

3a + 3t=75

a+t=75/3=25

and "a+t" is Joe's age, so Joe is now 25

this means if t years ago (when Joe was 17), Kate was half as old as Jean, that:

(17+t) + (b+t) + (2b+t)=113

3b+3t=113-17=96

b+t=96/3=32

and 'b+t' is Kate's age, so Kate is now 32

25+32+z=113

z=113-57=56


So Joe is 25, Kate is 32 and Jean is 56