SOLUTION: The sum of Jim's age and Mike's age is 52. Six years ago Mike was four times as old as Jim was. How old is Jim now? Could someone help me please?

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Question 120846: The sum of Jim's age and Mike's age is 52. Six years ago Mike was four times as old as Jim was. How old is Jim now?
Could someone help me please?
Found 2 solutions by checkley71, solver91311:
Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
J+M=52 OR J=52-M
(J-6)=4(M-6)
(52-M-6)=4M-24
46-M=4M-24
-M-4M=-24-46
-5M=-70
M=-70/-5
M=14 ANSWER FOR MIKE'S AGE NOW.
J=52-14=38 ANSWER FOR JIM'S AGE NOW.
PROOF
38-6=4(14-6)
32=4*8
32=32

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
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%28J-6%29. We also know that M%2BJ=52

M%2BJ=52 means that M=52-J. We can substitute this information into the other equation:

M-6=4%28J-6%29

%2852-J%29-6=4%28J-6%29

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%2A8=32, answer checks.