# SOLUTION: Margaret is 16 years younger than Alice. Alice is 3 times as old as Jonathan. A year ago, Alice's age was twice the sum of Margaret's and Jonathan's ages. How old is Margaret no

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 Question 333547: Margaret is 16 years younger than Alice. Alice is 3 times as old as Jonathan. A year ago, Alice's age was twice the sum of Margaret's and Jonathan's ages. How old is Margaret now?Answer by ankor@dixie-net.com(15622)   (Show Source): You can put this solution on YOUR website!let m = Margret's present age let a = Alice's present age let j = Jonathan's present age : Write an equation for each statement, simplify if possible: : "Margaret is 16 years younger than Alice." m = (a-16) : " Alice is 3 times as old as Jonathan." a = 3j : " A year ago, Alice's age was twice the sum of Margaret's and Jonathan's ages." a - 1 = 2[(m-1)+(j-1)} a - 1 = 2(m+j-2) a - 1 = 2m + 2j - 4 a = 2m + 2j - 4 + 1 a = 2m + 2j - 3 Replace m with (a-16 a = 2(a-16) + 2j - 3 a = 2a - 32 + 2j - 3 a - 2a = 2j - 32 - 3 -a = 2j - 35 a = -2j + 35; multiplied by -1 Replace a with 3j 3j = -2j + 35 3j + 2j = 35 5j = 35 j = j = 7 yrs, (Jon) then a = 3(7) a = 21 yrs, (Alice then m = 21 - 16 m = 5 yrs old, is Margaret's age : checking this out in the statement: " A year ago, Alice's age was twice the sum of Margret's and Jonathan's ages." 21 - 1 = 2(5 - 1 + 7 -1) 20 = 2(10), confirms our solution : How old is Margaret now? 5 yrs