Question 165896
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?