Question 894481: In a family, a couple has a son and a daughter. The age of the father is three times that of his daughter and the age of the son is half of his mother. The wife is 9 years younger to her husband and the brother is seven years older than his sister. What is the age of the mother?
(1) 40
(2) 50
(3) 45
(4) 60
(5) None of these
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Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 3. In a family, a couple has a son and a daughter. The age of the father is three times that of his daughter and the age of the son is half of his mother. The wife is 9 years younger to her husband and the brother is seven years older than his sister. What is the age of the mother?
(1) 40
(2) 50
(3) 45
(4) 60
(5) None of these
the mother is 60.
here's how it works, or at least one way that it works.
f = father's age
m = mother's age
s = son's age
d = daugher's age
f = 3d
s = m/2
m = f-9
s = d+7
that's what you start with.
you are looking for m.
from m/2 = s, you can solve for m to get m = 2s.
from s = d+7, you can replace s with d+7 to get m = 2(d+7) = 2d+14
from f = 3d and m = f-9, you can replace f with 3d and get m = 3d-9
you have m = 3d-9 and you have m = 2d+14
from this you get 3d-9 = 2d+14 and you can solve for d to get d = 23.
since f = 3d, you get f = 69
since m = f-9, you get m = 60
since s = d+7, you get s = 30
you get:
f = 69
m = 60
s = 30
d = 23
f = 3d becomes 69 = 3*23 which becomes 69 = 69 - this is good.
s = m/2 becomes 30 = 60/2 which becomes 30 = 30 - this is also good.
m = f-9 becomes 60 = 69-9 which becomes 60 = 60 - this is also good.
s = d+7 becomes 30 = 23+7 which becomes 30 = 30 - this is also good.
they're all good so the solution is confirmed as good.
the solution is that the age of the mother is 60.
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