# SOLUTION: Three years ago, Joe's age was 1 year more than twice Karen's. Six years from now, his age will be 10 years more than half her age. how old is Joe?

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 Question 429528: Three years ago, Joe's age was 1 year more than twice Karen's. Six years from now, his age will be 10 years more than half her age. how old is Joe?Answer by stanbon(57323)   (Show Source): You can put this solution on YOUR website!Three years ago, Joe's age was 1 year more than twice Karen's. Six years from now, his age will be 10 years more than half her age. how old is Joe? ------- Equations: (j-3) = 2(k-3)+1 (j+6) = (1/2)(k+6)+10 ----- Rearrange the 1st equation: j-3 = 2k-6+1 j-3 = 2k-5 j = 2k-2 --- Substitute into the 2nd equation and solve for "k": (2k-2+6) = (1/2)(k + 6) + 10 Multiply thru by 2: 2(2k+4) = k+6+20 4k+8 = k+26 3k = 18 k = 6 (Karen's age now) --- Solve for "j": j = 2k-2 j = 12-2 j = 10 (Joe's age now) =========================== Cheers, Stan H. ===============