Question 120846
Let's say Jim's age now is J and Mike's age now is M.  Six years ago, Mike was then M - 6, and Jim was J - 6, but we know that {{{M-6=4(J-6)}}}.  We also know that {{{M+J=52}}}


{{{M+J=52}}} means that {{{M=52-J}}}.  We can substitute this information into the other equation:


{{{M-6=4(J-6)}}}


{{{(52-J)-6=4(J-6)}}}


Now all we have to do is simplify and solve:


{{{46-J=4J-24}}}


{{{-J-4J=-24-46}}}


{{{-5J=-70}}}


{{{J=14}}}


That answers the question, but we have to check our work:


{{{52-14=38}}}, so Mike must be 38 now.


Six years ago, Mike was 32, and Jim was {{{14-6=8}}}, and {{{4*8=32}}}, answer checks.