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 .