SOLUTION: The sum of the ages of a woman and her son is 64 years. In 4 years time the woman will be three and half times as old as her son. How old were they three years ago?

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Question 1139422: The sum of the ages of a woman and her son is 64 years. In 4 years time the woman will be three and half times as old as her son. How old were they three years ago?
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

let the age of a woman be w and her son’s age be s
given:
w%2Bs=64
w=64-s.....eq.1
in 4+years time the woman will be 31%2F2=3.5 times as old as her son:
w%2B4=3.5%28s%2B4%29
w=3.5s%2B14-4
w=3.5s%2B10........eq.2
from eq.1 and eq.2 we have:
64-s=3.5s%2B10
64-10=3.5s%2Bs
54=4.5s
s=54%2F4.5
s=12=> her son’s age now
w=64-s.....eq.1
w=64-12
w=52=>the woman’s age now
How old were they three years ago?
s=12-3=9=> son’s age three years ago
w=52-3=49=> woman’s age three years ago