#### CHECK OUT SHMOOP'S FREE STUDY TOOLS: Essay Lab | Math Shack | Videos

# Algebraic Expressions

# Independent and Dependent Variables

Let's take a closer look at how independent and dependent variables work by working through some examples:

### Sample Problem

Jim gets paid $10 per hour. The amount Jim gets paid in a week depends on the number of hours he works that week. If all he did was put in two hours shelving books at the library, he will barely be able to afford to buy a book. Good thing he works at the library. On the other hand, if he works 12-hour days in the assembly line of an automobile factory, he can afford to buy all the books he wants. Same rate (input), different pay (output).

### Sample Problem

Jim gets paid $10 per hour. The amount Jim gets paid in a week depends on the number of hours he works that week. Let *p* represent the amount Jim gets paid in a week. Let* h* represent the number of hours Jim works that week. Then *p* = 10 · *h*.

The letters *p* and *h* are called variables because they are not fixed numbers. This fact reminds us: Be sure to have your numbers spayed or neutered. The quantity *h* varies because Jim may work a different number of hours each week. The quantity *p* varies because *p* depends on *h*.