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.

## Example

Let’s look at another example.

Jimmy’s fish tank has either red or blue fish in it. Right now, there is a total of 12 fish in the tank. If 8 of them are blue fish, how many of them are red fish?First, you need to write your algebraic equation.

What do you do? Yes, you read through the problem carefully to get a feel of what is going on and what is being asked. Doing so, you see that the total number of fish in the tank is 12. The total number of fish is the addition of blue fish and red fish. The problem tells you there are 8 blue fish, and it wants you to find the number of red fish.

So, the number of red fish is your unknown number, your variable. You write your algebraic equation as *x* + 8 = 12. To solve this problem, you need to subtract the 8 from both sides of the equation. Doing this, you get *x* + 8 – 8 = 12 – 8. Evaluating, you get *x* = 4. Since *x* represents the number of red fish in Jimmy’s tank, you know that Jimmy has 4 red fish in the tank.

## Lesson Summary

Let’s review what you’ve learned. **Word problems** are math problems given in words, often given as real-life scenarios. In order to solve word problems, you first need to write an algebraic equation from the problem. An **algebraic equation** is a mathematical statement using numbers, variables, and symbols that includes an equals sign.

Once you fully understand what the problem is telling you and what it is asking of you, then you can write an algebraic equation to represent the scenario. To solve your algebraic equation, you perform any necessary inverse operations to both sides of the equation to isolate your variable. Because this lesson focuses on addition problems, your inverse operation will be subtraction. So, you subtract what is being added to the variable from both sides of the equation to find your answer in terms of the original word problem.

## Learning Outcomes

Read and work through the examples in this lesson and strengthen your capacity to:

- Relate a word problem to a real-life scenario
- List the components of an algebraic expression
- Convert an addition word problem into an algebraic expression
- Solve the equation to find an unknown