Purple math age word problem example

[upspin]

Hello.

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?

[stapel_eliz]

...can it be solved using one variable?

Certainly! Instead of using variables for each of the original ages, define the other age in terms of the variable for William's age!

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.

You did nothing wrong. The "author" was an idiot!