Emily is twice as old as Matt. Three years ago, she was three times as old as he was. How old is Matt now?

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m = matts age nowm-3  = matts age 3 years ago2m = emilys age now2m-3 = emilys age 3 years ago.  It's 3 times larger than matts age was then so: 2m-3 = 3(m-3) = 3m-9   Add 9 and -2m to both sides.  9-3 = 3m - 2m6 = m.  Matt is current 6 years old and Emily is currently 12 years old.  Three years ago Emily was 9 and Matt was 3.  Three times Matt's age then is 9 which is Emily's age 3 years ago!