Solution

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The question is about Karen's age. What is it? We do not know yet, but we are going to find out. Until we did, let's introduce a variable x to denote the unknown age. So, Karen's age is x. What do we know about x?

We know that Karen is twice as old as Lori, which means that Lori's age is x/2. Three years from now Karen is going to be and Lori . The sum of their years at the time will be (x + 3) + (x/2 + 3) = . Let's multiply the whole equation by 2: (2x + 6) + (x + 6) = . This simplifies to:

or

or

Karen is then 24 years old (And I thought the girls were school age!) and Lori is half that: years old.

Let's check: three years from now Karen will be and Lori . Together this gives . Quite right.

There are other ways to work out the problem. To avoid working with fractions, it is easier to start with Lori's age, although you are not actually asked to find it. So let's y be Lori's age. Then Karen is 2y years old. Three years from now they will be y + 3 and 2y + 3, which together must be 42:

which simplifies to

or

and finally

So Lori is 12 years old, and Karen who is twice as old is .