3.1+Variables+and+Constants

Section 3.1 - Variables and Constants
Suppose your grandma gets a cell phone and doesn't need unlimited minutes. Instead, she pays a monthly fee of $5 and four cents for each minute she uses. She asks you how much money she will have to pay each month. How can you explain that to her?

Obviously the amount she will pay each month depends on how many minutes she uses, even though the $5 is going to be the same each month. The formula is represented by the equation Cost = M + 5, where M represents the number of minutes.

The M is called a ** Variable **, a place holder that represents an amount that can vary - one month it might be 20 and the next it could be 350.Variables are generally represented by letters, x is the most common, but any letter could be used.

The 5 in this example is called a ** Constant **, an amount that does not vary or change - it will always be $5 each month.


 * What do the Letters Mean?**

Variables are generic enough that you can use whatever letter you want to represent an unknown or variable amount. However, it makes sense to use the first letter of the term you are representing. If you were ordering some number of pizzas and drinks, you might describe those using the letters "p" and "d". You could also use "x" and "y", but somehow you would need to remember which is which so that you don't mix them up.

However, some letters have gained a fairly high degree of common acceptance. The formula "d=rt" means distance = rate (time), which uses the first letters of those terms. Other variables will be introduced as you go through math: the slope of a line will be called "m", "b" will be the y-intercept on a graph.


 * The Coefficient is Something Else**

Say you're going to the store to buy apples. You want 4 bags of apples and then 6 more single apples. Although you don't know how many apples there are in each bag, you can assume that there are the same number in each bag. So, the expression could be written as 4b + 6. The variable "b" represents "bags" of apples, and the 6 (constant) is the six single apples. But look at the "4" in that expression. It is kind of like an adverb in a sentence - it relates to the variable, but not really to the constant. But it isn't a variable either, because it will always be 4. So it isn't either one. It is called a Coefficient. **A Coefficient is a number (could be an integer, fraction, decimal) that comes before the variable.** In the expression, 8y - 5, 8 is the coefficient of y.

**Where to from here?**
3.1 Variables and Constants 3.2 Terms 3.3 Equations 3.4 Formulas 3.5 Solving for X 3.6 Two Unknown Relative Values Chapter Three Summary Chapter Three Homework