Charlie is 57 and Pat is the oldest person in the world (116). In two years time, Charlie will be 59, and Pat will be dead.

Seriously though, the problem is that there is no single solution - and only the teenager statement does anything to narrow things down. Charlie could be any age { 0 <= C <= 5}.

If Charlie were one year older, he would be half Pat's age.
C+1 = P/2
2(C+1)=P
2C=P-2
C=P-1

In two years, he will be half her age then. How old are they now?
C+2 = (P+2)/2
2(C+2)=P+2
2C+4=P+2
2C=P-2
C=P-1