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Solving Multiplication Word Problems with Two or More Variables

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  • 0:02 Multiplication Word Problem
  • 0:53 Writing the Equations
  • 2:16 Solving the Equations
  • 3:37 Example
  • 5:56 Lesson Summary
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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

After viewing this video lesson on how to solve multiplication word problems, you will know how many equations you need to work with for each problem as well as how to solve them. You will also have a chance to practice what you learned with a quiz.

A Multiplication Word Problem

Math is useful not just to get you through school but also in real life. In this video lesson, you will learn about solving multiplication word problems with two or more variables. These are math problems that include the multiplication operator and more than one unknown value. You will come across these problems not only on your math classes but also possibly in your real life. For example, you just might come across a problem such as this when building a home.

Sam has been hired to help build a home. He is working on the living room. The people who are going to be living in the home have told Sam that they want the length of the living room to be two times longer than the width. They also want the living room to have an area of 450 square feet. Sam needs to figure out the dimensions of this living room so he can get started on his building work.

Writing the Equations

Before you can solve this problem, you need to write your equations. I know word problems can be scary to work with, but as long as you take your time to carefully read the problem and fully understand what is going on and what is asked of you, then you will find that solving these problems aren't as scary as they may seem at first. So, take your time and carefully read the problem again.

Try to visualize in your head what is going on: picture Sam standing in an imaginary living room looking at the walls to try to figure out how long they need to be. Now, use your knowledge of math to come up with equations that tell you what is going on.

One key point with these problems is that you will have more than one equation. For every unknown value or variable that you have, you will have one equation. So, in this case, since you have two unknown values - the length and the width - you will have two equations. The first equation that you see is the one where the problem says that the length of the living room is two times the width of the living room. This you can write as l = 2w. You have used l for the length and w for the width. Now, the second equation is where the problem says that the area equals 450 square feet. This you write as lw = 450.

Solving the Equations

Now that you have your two equations, you can now proceed with solving. You see that your first equation is already solved for the l variable. This indicates that you can use the substitution method to help you solve this problem. You can substitute the first equation into the second equation. By doing this, you will have created an equation with only one variable that you can solve for. There are other methods that you can use and these methods are discussed in other lessons.

(2w)w = 450

2w^2 = 450

You use your math skills to go ahead and solve this problem for the w variable. You divide both sides by 2, and then take the square root of both sides to isolate your variable.

2w^2 = 450

2w^2 / 2 = 450 / 2

w^2 = 225

w = 15

You find that your w is equal to 15. So, that means that the width of the living room is 15.

Now that you've solved for w, you can now go and solve for the other variable. You can plug in your answer for w into the first equation to solve for the l variable.

l = 2w

l = 2(15)

l = 30

Your l, your length, is equal to 30. Now you are done!

Example

Let's look at another example.

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