Question 163677
Kathy,

This is a typical age word problem.  You will see lots of them in math courses.

Your Question:

Tom is twice as old as Jill. In 6 years, Tom will be half again as old as Jill. How old are Tom and Jill?

The question does not give us Jill's age.  I will use J to represent Jill.
You could use any letter but J is easier to connect with Jill.

So, let J = Jill.

Tom is twice as old as Jill.

So, let Tom = 2 times J or simply 2J

We are now going into the future exactly 6 years.  

This means they both will be 6 years older.

Do you agree?

Jill's age 6 years from now = J + 6

Tom's age 6 years from now = (1/2)(J)

We equate J + 6 = 2J + (1/2)(J) and solve for J.

By the way, we can write (1/2)(J) as J/2...they both mean the same thing.

Back to your question.

J + 2 = 2J + J/2

We want to remove the fraction J/2.  It's easier working without fractions.

To do so, multiply each term on both sides of the equation by 2.

2 times (J + 2) = 2J times(2) + 2 times(J/2)

We now have this:

2J + 12 = 4J + J

2J + 12 = 5J

12 = 5J - 2J

12 = 3J

12/3 = J

4 = J

At the beginning, I said that J = Jill's age.

So, Jill is 4 years old.

I also said that Tom's age is 2J.

So, Tom's age = 2(4) or 8 years old.

Did you follow?