In this video we will be learning how to declare variables in word problems. After you finish this lesson, view all of our Algebra 1 lessons and practice problems.

## Example of Declaring Variables in Algebra

The length of a rectangle is 5 units longer than the width. If the perimeter is 22 units, how long is the width?

Let

Let

Perimeter Formula:

## Examples of Declaring Variables

### Example 1

Linda spent for notebooks; a box of pencils at and a box of pens at . What is the price of each notebook?

First, declare variables

Let = cost of each notebook

Next, use sentence to create equation

Now, we can solve for

Add the constants on the right side

Then subtract to both sides of the equation.

To solve , let’s divide both sides by

Therefore, the cost of each notebook is

### Example 2

Krishna bought a total of pens. She bought more boxes of colored pink pens than of colored red pens. How many of each did she buy?

First, declare variables

Let = for colored pink pens

Let = colored red pens

Next, use sentence to create equation

Since p has more pens than , therefore:

Substitute the values of to the equation

Now, we can solve for

3

Then subtract to both sides of the equation.

To solve , let’s divide both sides by

Therefore, there are colored red pens.

Let’s go back to the problem and substitute the value of .

## Video-Lesson Transcript

Let’s go over declaring variables.

When we have word problems, we may start writing down equations based on the given then try to solve it.

But if we lost track of what the variables are, it’s highly possible to get an incorrect answer.

Normally, declaring variables is like this:

Let equal a number of something.

Or let equal the width of a shape.

Let’s have an example.

A book store charges for the first book and for each additional book. Write an expression to represent the total cost of buying any number of books.

Let’s start with declaring the variables.

Let number of books.

Now we need to know the total cost based on the information given.

Now, we have

cost times number of additional books

Let’s use in this equation.

cost

is the number of additional books. So we subtract the first book from cost .

For example:

We bought books. The cost is going to be additional.

It’s not because the first book is valued at .

Let’s take a look at another example.

The length of a rectangle is units longer than the width. If the perimeter is units, how long is the width?

Let

Let

Now, let’s draw a rectangle.

Label the two as “w” for width and label the length as ““.

The perimeter is

Since we already labeled the rectangle, it’ll be easier.

Let’s continue solving

Then subtract to both sides of the equation.

This becomes

To solve ““, let’s divide both sides by

Now, let’s go back to the problem and substitute the value of .

If ,

then the .