SOLUTION: A’s mother is twice as old as A’s brother. A is 6 years yqunger than his brother but 4 years older than his sister. If A’s sister is 15 his mother’s age is:

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Question 812426: A’s mother is twice as old as A’s brother. A is 6 years yqunger than his brother but 4 years older than his sister. If A’s sister is 15 his mother’s age is:
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
Let m = mother's age
Let b = brother's age
Let a = A's age
Let s = sister's age

With four variables we will need 4 equations. From "A’s mother is twice as old as A’s brother" we get:
m = 2b
From "A is 6 years younger than his brother" we get:
a = b - 6
From "A is ... 4 years older than his sister" we get:
a = s + 4
From "A's sister is 15" we get:
s = 15

A system of four variables and four equations is often difficult to solve. But this one is easy. Using the last equation we can substitute for s in the 3rd equation:
a = (15) + 4
which gives us:
a = 19
Using this result and the second equation we can substitute for a:
(19) = b - 6
which gives us:
25 = b
Using this result and the first equation we can substitute for b:
m = 2(25)
which gives us
m = 50
So the mother is 50 years old.