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