SOLUTION: Fred is 3 yrs. older than his sister Mary. In 7 yrs she will be 6/7 of his age. How old are they?

Question 165896: Fred is 3 yrs. older than his sister Mary. In 7 yrs she will be 6/7 of his age. How old are they?
Answer by midwood_trail(310) (Show Source): You can put this solution on YOUR website!
Fred is 3 years older than his sister Mary. In 7 yrs she will be 6/7 of his age. How old are they?
Mary's age now = x
Fred's age now = x + 3
In seven years each person will be 7 years older, right?
Here's how we represent that:
Mary = x + 7
Fred = (x + 3) + 7
We now multiply (6/7) times Fred's age 7 years form now.
The equation looks like this:
x + 7 = (6/7)(x + 3) + 7
We multiply every term by 7 (our LCD).
Doing so, we get this:
7x + 49 = 6x + 18 + 49
We now combine like terms:
7x - 6x = -49 + 67
x = 18
Mary is 18 years old.
Fred is 18 + 3 = 21 years old.
Did you follow?
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