Rearranging Variables

Date: 10/01/98 at 18:57:29
From: Pacey Barron
Subject: Using variables

Dear Dr. Math,

How come when you use a variable in a problem sometimes the answer 
still has a variable, and you can not get an actual number answer?

Date: 10/02/98 at 11:39:15
From: Doctor Peterson
Subject: Re: Using variables

Hi, Pacey. I assume you are not talking about making a mistake in 
solving the problem. If there is only one variable in the original 
equation, then either you can solve it with a numerical answer, or you 
simply can't solve it - there would be no actual solution that still 
involved the variable.

But if you are given an equation with two variables in it, like 
C = 2*pi*r, and are told to solve it for one of the variables, say 
r = C/(2*pi), then the other variable will still be there. In this 
case, you are simply rearranging a formula for a different use. As 
given, the formula lets you get the circumference of a circle given 
its radius. After you solve it for r, it lets you find the radius of a 
circle given its circumference. You don't know either one yet, but if 
I gave you a circumference, you could plug it right into this formula. 
If you hadn't already solved for r, you would have to put my value into 
the original equation for C and then solve that for r.

So there are two ways a variable can be used. Sometimes it is an 
unknown, which you want to figure out from the equation. Other times 
it just stands for a value that you don't know now, but will know 
later, like C in my example. Then you just work with it as if it were 
a value, but without being able to do the calculations. When you're 
done, you can replace it with any value.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/