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Algebraic Expressions

Algebraic Expressions

At a Glance - Evaluating Formulas by Substitution


As we mentioned, a formula has a dependent variable on one side and an expression involving the independent variable(s) on the other side. To evaluate a formula, we evaluate the expression containing the independent variable(s). The result is the value of the dependent variable. Ready, Miss Independent? Let's make you Miss Dependent.

Sample Problem

Consider the formula C = 5xy. Find C if x = 2 and y = 3.

Since C is the dependent variable, that'll be our result. Now, how do we find its value? We evaluate the expression on the other side of the equal sign, 5xy, for x = 2 and y = 3.

C = 5(2)(3) = 30

We now know C's value is 30. However, we don't know if that's in dollars or pesos—no getting excited just yet.

We can use formulas to answer all sorts of questions. Like, "Why is the sky blue?" or "What makes birds sing?" or "What happened to Julia Stiles' career?" More practically, they can help us solve something like the problem below.

Sample Problem

Find the area of a square with sides that are 4 cm long.

The area of a square is given by the formula A = s2, where A is the area of the square and s is the length of a side. In this case, the length of a side is 4, and we substitute 4 for s and evaluate the area formula:

A = (4)2 = 16 cm2

We will now let r represent rock star, which is what we are for finding the area of this square.

Example 1

Sara has a clock with a circular face. She wants to glue a ribbon around the outer edge of the face of the clock. 

Heaven knows why she thinks this will look good. It would be enough to make Martha Stewart have a conniption fit. Ah, well. To each her own.

If the face of the clock has a radius of 5 inches, how much ribbon will Sara need to complete her aesthetic disaster?


Exercise 1

Zach has a rectangular living room that measures 10 feet wide by 20 feet long. He's thought about bringing in some furniture, but he doesn't want to spoil the perfect rectangularness of it. In order to cover the floor of his living room with carpet, how many square feet of carpet does Zach need?


Exercise 2

Zach has a rectangular living room that measures 10 feet wide by 20 feet long. How much trim will Zach need if he wants to put trim all around the edge of the floor?


Exercise 3

What is the area of the triangle shown below? No fair guessing. We know what a lucky guesser you are.


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