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Solving Division Word Problems with Two or More Variables

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  • 0:00 A Division Word Problem
  • 0:41 Writing the Equations
  • 1:24 Solving the Equations
  • 2:12 Example
  • 3:53 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.

Watch this video lesson to learn how you can solve division word problems that involve more than one variable. Learn how many equations you need to be able to solve your problem.

A Division Word Problem

In this video lesson, you will learn how to solve division word problems with two or more variables. These are math problems written in words that involve the division operator and have more than one variable. You will want to learn how to solve these types of problems because you will come across these on your math tests, and you might come across them in real life.

As you continue in your math lessons, you just might come across a problem such as this on a test: Sally is thinking of two numbers. The first number divided by 3 is equal to 2. The second number is the first number divided by 3. What are these two numbers?

Writing the Equations

In order to solve this problem, you first need to write out your equations. There is one big difference that you have to keep in mind here. For every variable that you have, you will need to write one equation.

Look at your problem. How many variables or unknown values do you have? You have two. You have the first number and the second number. This tells you that you need to write two equations.

Now, carefully read through your problem to figure out what your two equations are. You have decided to use x for the first number and y for the second number. Reading through your problem, you see that the first equation is x / 3 = 2. The second equation then is y = x / 3.

Solving the Equations

Now that you have your two equations, you can go ahead and solve them. There are several methods that you can use. These are discussed in other lessons. Looking at your two equations, you see that you can use the substitution method to solve. Other solving methods are discussed in other lessons. You can solve the first equation for x and then use that information in the second equation to solve for y.

Solving the first equation for x gives you this:

x / 3 = 2

(x / 3) * 3 = 2 * 3

x = 6

Plugging this into the second equation and solving for y gives you this:

y = x / 3

y = 6 / 3

y = 2

And you are done. Your complete answer is x = 6 and y = 2.

Example

Let's look at another example. Larry has created a brainteaser for his friends to figure out the number of marbles he has. Larry tells his friends that he has both red and blue marbles. The number of red marbles divided by 2 is equal to 8. And the number of red marbles divided by blue marbles is 4. How many blue marbles does Larry have?

Reading carefully through this problem, you see that you have two variables. This means that you need two equations. You decide to use r for the number of red marbles and b for the number of blue marbles. Using these two variables, you write these two equations based on the problem.

r / 2 = 8

r / b = 4

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