# SOLUTION: My algebra teacher gave us this problem, I don't know how to start solving it. Please help me. Marty is 1/3 as old as her mother. Five years ago she was only 1/5 of the age of her

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 Click here to see ALL problems on Age Word Problems Question 333745: My algebra teacher gave us this problem, I don't know how to start solving it. Please help me. Marty is 1/3 as old as her mother. Five years ago she was only 1/5 of the age of her mother. How old is Marty?Found 2 solutions by ankor@dixie-net.com, Edwin McCravy:Answer by ankor@dixie-net.com(15666)   (Show Source): You can put this solution on YOUR website!Let m = mother's present age Let d = daughter's present age (Marty) : Write an equation for each statement: ; Marty is 1/3 as old as her mother. d = m or we can say m = 3d : Five years ago she was only 1/5 of the age of her mother. d - 5 = (m-5) Mult both sides by 5, get rid of that fraction 5(d-5) = m - 5 5d - 25 = m - 5 5d = m - 5 + 25 5d = m + 20 Replace m with 3d 5d = 3d + 20 5d - 3d = 20 2d = 20 d = 10 yrs is Marty : : check solution in the statement; m = 3(10) = 30 is mom "Five years ago she was only 1/5 of the age of her mother. 10 - 5 = (30 - 5) Answer by Edwin McCravy(8920)   (Show Source): You can put this solution on YOUR website!My algebra teacher gave us this problem, I don't know how to start solving it. Please help me. ``` Let X = Marty's age now Let Y = Mother's age now Then Marty's age five years age = (X-5) Mother's age five years ago = (Y-5) 1/3 of Mother's age now = 1/5 of Mother's age five years ago = ``` >>...Marty is 1/3 as old as her mother. ``` Marty's age = 1/3 of Mother's age now X = ``` >>...Five years ago she (Marty) was only 1/5 of the age of her mother...<< ``` Marty's age five years ago = 1/5 of Mother's age five years ago (X-5) = So we have these two equations Multiply both sides of the first equation by 3 to clear of fractions. Multiply both sides of the first equation by 5 to clear of fractions. Canceling clears fractions: Simplifying further: Simplifying further: Since the first equations tells us that Y = 3X we can replace the Y in the second equation by 3X So Marty is 10 years old. However we need to find her Mothers age so we can check. We use Y = 3X Y = 3(10) Y = 30 So her mother is 30. Let's check: Marty is 1/3 as old as her mother. Indeed 10 is 1/3 of 30 Five years ago she was only 1/5 of the age of her mother Five years ago se was 5 and he mother was 25, and indeed 5 is 1/5 of 25. So we know we are right. Edwin```