Three years ago, Jim was half as old as Tom. Three years from now, Jim will be half as old as Michael. If Jim's age now is half as old as Michael's age three years ago, How old are Jim, Tom and Michael at present?

Question

Three years ago, Jim was half as old as Tom.  Three years from now, Jim will be half as old as Michael.  If Jim's age now is half as old as Michael's age three years ago,  How old are Jim, Tom and Michael at present?

Steve · Answer

Just translate the words to symbols:

j-3 = (t-3)/2
j+3 = (m+3)/2
j = (m-3)/2

Unfortunately, those three equations do not determine their ages uniquely.

Jim,Tom,Michael could be
4,5,11
5,7,13
6,9,15
. . .

I suspect a typo in the problem.