Solving Word Problems with Algebraic Addition Expressions

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  • 0:00 A Word Problem
  • 0:40 Writing the Expression
  • 1:30 Solving It
  • 2:25 Example
  • 3:20 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 going over this lesson, you will be able to solve addition word problems. You will know how to write an algebraic expression that you can solve to find your answer.

A Word Problem

Word problems could be your worst enemy, or they could be the key to your passing your next math test. A word problem is a math problem written with words. You won't have an already written math expression to solve for. You'll need to come up with and write it yourself. Let's take a look at how we can do this with the help of this word problem.

Hannah is shopping for her little brother. Currently, she has $14 in her shopping cart. She came to the store with $25 in her wallet. What is the amount she can add to her $14 to reach her total of $25?

In this lesson, we will focus on addition word problems, those word problems that use the addition operator.

Writing the Expression

Before going ahead and solving this problem, we need to write an algebraic expression. To do this, we need to carefully read our problem so we know exactly what is going on and what we need to do. Reading carefully through this problem, we see that it is an addition problem. It is asking us what number plus $14 will get us to $25. How can we write this as a mathematical algebraic expression?

We can write it like this:

14 + x = 25

The variable x stands for the amount that we are looking for. This is the amount that when we add it to $14 will get us to $25. As you can see, we have added our variable to the 14 and we made it equal to 25. This is what we want. We want a number that equals 25 when added to 14.

Solving It

Now that we have our expression, we can find our answer by solving it for the variable. We will use our algebra equation solving skills to isolate our variable. We see that our variable is added to a 14. To isolate the variable, we will perform the inverse operation. The inverse operation to addition is subtraction. So, we will subtract the 14 from both sides of the equation.

We need to perform the same operation to both sides of our equation in order to keep our equation the same so we will get the correct answer. Subtracting 14 from both sides, we get 14 + x - 14 = 25 - 14. This turns into x = 11. Our answer is $11. Hannah can spend $11 more before reaching her total of $25.

Example

Now, try this problem.

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