Example

When walking, Jose burns 96 calories per mile and Sara burns 64 calories per mile. One day the two of them walk a total of 7 miles. Let $x$ represent the number of miles walked by Sara.

1. Write an algebraic expression for the total number of calories burned by the two of them.
2. Together they burn a total of 505.6 calories. How far did each person walk?

Solution

In order to solve application problems like this one, it helps to carefully read and reread the problem. Do not expect to completely understand the problem after a single (or even double!) reading. Read slowly and take notes as you go. I'll try to illustrate my thought process...

The first thing I read is that when Jose walks, he burns 96 calories per mile. From this I get that

The first sentence also tells us that

Now, this is kind of obvious, but I'll say it anyway:

Let's hold on to that thought as we continue reading through the problem...

Sara and Jose walk a total of $7$ miles. Of those $7$ miles, Sara walks $x$ of them. The variable $x$ must represent some number between $0$ and $7$. But the crucial idea here is that if Sara walks $x$ miles, then Jose must walk $7-x$ miles. Do you understand that? Jose walks the "leftover" miles after Sara walks her $x$ miles. Their total is $7$.

So here is what we have found:

or

The final expression writes $CJ$ and $CS$ in terms of the variable $x$. That expression is the answer for part 1.

To solve part 2, we use the fact that the total calories are given to write an equation:

This equation has the single solution $x=5.2$. (Work through the details on your own!) This means that Sara walked $5.2$ miles and Jose walked $7-5.2=1.8$ miles.