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Solving Subtraction Word Problems with Two or More Variables

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  • 0:02 A Subtraction Word Problem
  • 1:42 Writing the Equations
  • 2:33 Solving the Problem
  • 3:43 Example
  • 5:10 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 word problems that involve the subtraction operation and more than one unknown value. Learn how many equations you will need to create and how to solve them.

A Subtraction Word Problem

In this video lesson, you will learn how to solve subtraction word problems with two or more variables. These are math problems written in words that involve the subtraction operator and that have more than one unknown value. It is these unknown values that you need to solve for.

Why do you need to learn about solving these types of problems? It is important to learn how to solve these problems because you will come across these types of problem not only in your math class but also in real life. Being able to solve these types of problems when you need to is a good skill to have.

One interesting thing about these subtraction word problems with two or more variables is that you will actually end up working with more than one equation. You will need one equation for each unknown value. So, if your problem has three unknown values, then you will end up working with three equations. Because you are working with word problems, you will need to create these equations from the problem. You will need to fully understand the problem, what is going on, and what is being asked of you before writing the equations.

Let's take a look at a possible problem that you might encounter: Sarah has just received a box of chocolates from a dear friend. Her friend tells her that inside the box there are two kinds of chocolate: milk and dark. There are more milk chocolates than dark chocolates. Subtracting the number of dark chocolates from the number of milk chocolates gives 5 as an answer. The number of milk chocolates is twice that of dark chocolates. How many milk chocolates are there?

Writing the Equations

Before you can solve your problem, you need to write out your equations. You see that you have two unknown values, the number of milk chocolates and the number of dark chocolates. You can label your unknown values with a d for dark chocolates and an m for milk chocolates. Since you have two unknown values, you need to have two equations. Reading your problem carefully, you see that your two equations can be found from two of the sentences in your problem.

The first equation can be found in the sentence that tells you how many chocolates you get after subtracting the number of dark chocolates from the number of milk chocolates. Using these as your variables, your first equation can be written as m - d = 5. The second equation can be found in the sentence directly after. Your second equation can be written as m = 2d.

Solving the Problem

Now that you have your two equations, you can solve your problem. Looking at your two equations, you see that you can use the substitution method to solve. There are other methods of solving problems with more than one equation, and these are discussed in other lessons. Using the substitution method, you see that you can substitute the second equation into the first equation. This way you are left with an equation with just one variable.

2d - d = 5

This is an equation that you can easily solve for. Combining your like terms, you get this:

d = 5

Look at that! You have just solved for the number of dark chocolates. But what does your problem want you to solve for? Reading the problem again, you see that the problem wants you to find the number of milk chocolates. So, you are not done solving your problem just yet. Now you need to solve for the number of milk chocolates. To do this, you can use the second equation and plug in the answer for d.

m = 2d

m = 2 * 5

m = 10

The answer is 10. There are 10 milk chocolates in the box.

Example

Let's look at another example. James has a bag of marbles. Inside there are both red and blue marbles. The number of red marbles equals the number of blue marbles minus 4. There are twice as many blue marbles as red marbles. How many blue marbles are there?

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