# Writing & Solving Addition Word Problems with One Variable

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• 0:01 Addition Word Problem
• 0:38 Writing Your Algebraic…
• 2:13 Solving Your Problem
• 3:17 Example
• 4:24 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 watching this video lesson, you will be able to write and solve addition word problems. Learn how to read your word problem, write out the algebraic equation, and then solve it for the unknown variable.

## Addition Word Problem

In this video lesson, you will learn how to take a word problem that you are given, understand it, write out the algebraic equation, and then solve it to find your answer. In this lesson, we focus specifically on addition word problems. Word problems are math problems given in words. Usually, they best describe a real-world scenario that you can picture in your head, and they will ask you to find an unknown number. For example, you might see the following: 'Suzie and Jenny together have \$50 to go out for a nice dinner together. If Suzie put in \$23, how much did Jenny put in?'

## Writing Your Algebraic Equation

In order to solve this problem, you first need to turn this problem into an algebraic equation. An algebraic equation is a mathematical statement using numbers, variables, and symbols that include an equals sign. Yes, you need to write an algebraic equation for the given information. To do this, you need to fully understand the problem. Try to visualize what is going on in the problem. Once you fully understand what is going on and what is being asked, then you can go ahead and write out your algebraic equation, putting in as much of the given information as possible.

Reading through the problem, you see that the problem tells you that the combined amount from both Suzie and Jenny is \$50. What does it mean to be combined together? It means that there are things that have been added together. In this case, you're adding money, one amount from Suzie and another amount from Jenny.

What else does the problem say? It says that Suzie's part is \$23. It asks about Jenny's part. So, Jenny's part is the unknown number that you need to find, or the variable. Now you have all the information you need to write your algebraic equation. You use an x for Jenny's portion. You know you are supposed to add Suzie's and Jenny's portions together and that their total equals \$50, so you write 23 + x = 50. Looking at what you just wrote, you see that it expresses the same thing the problem does. You are adding Suzie's and Jenny's portions together, and the total should equal \$50.

## Solving Your Problem

Now that you have your algebraic equation, you can go ahead and solve it. You want to isolate the variable, the x in this case, so that it is by itself. To do this, you look to see what numbers are currently attached to the variable. Then you perform the inverse operation to both sides of the equation to detach the numbers from the variable. This inverse operation must be performed on both sides of the equation to get a correct answer. Because your problem is an addition problem, the inverse operation here is subtraction.

So, you subtract whatever is being added to the variable from both sides of the equation. Then you evaluate the problem to get your answer. You see that right now you have a 23 being added to the variable. This means that you need to subtract 23 from both sides. 23 + x - 23 = 50 - 23. Evaluating this, you get x = 27. Your answer is 27. Our variable represents Jenny's part, so you know that Jenny's contribution to the nice dinner fund is \$27.

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