My question regards the first age example problem on this page (http://www.purplemath.com/modules/ageprobs.htm).

In January of the year 2000, I was thirteen times as old as my son William. In January of 2009, I was four times as old as him. How old was my son in January of 2000?

The author uses 2 variables to solve this problem however, can it be solved using one variable?

I tried and my answer did not match the answer when using 2 variables to solve the problem.

Here's what I did when using x as William's age.

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`Age now Age in 9 years`

Elizabeth 13x 4(x+9)

William x (x+9)

Setting up my equation, I get:

13x = 4(x+9)

13x = 4x + 36

9x = 36

x = 4

So, William's age was 4 in January of 2000. But the author uses 2 variables for the problem and comes up with the age of 3.

What did I do wrong in using just one variable?