In algebra word problems are commonplace, though they confuse many. Use this free lesson to help you learn how to solve word problems.

A **word problem** is a math problem written out as a short story or scenario. Basically, it describes a realistic problem and asks you to imagine how you would solve it using math. If you've ever taken a math class, you've probably solved a word problem. For instance, does this sound familiar?

Johnny has **12** apples. If he gives **four** to Susie, how many will he have left?

You could solve this problem by looking at the numbers and figuring out what the problem is asking you to do. In this case, you're supposed to find out how many apples Johnny has left at the end of the problem. By reading the problem, you know Johnny starts out with **12** apples. By the end, he has **4 **less because he gave them away. You could write this as:

12 - 4

**12 - 4 = 8**, so you know Johnny has **8** apples left.

If you were able to solve this problem, you should also be able to solve algebra word problems. Yes, they involve more complicated math, but they use the same basic problem-solving skills as simpler word problems.

You can tackle any word problem by following these five steps:

**Read**through the problem carefully, and figure out what it's about.**Represent**unknown numbers with variables.**Translate**the rest of the problem into a mathematical expression.**Solve**the problem.**Check**your work.

We'll work through an algebra word problem using these steps. Here's a typical problem:

The rate to rent a small moving van is $30 per day, plus $0.50 per mile. Jada rented a van to drive to her new home. It took two days, and the van cost $360. How many miles did she drive?

It might seem complicated at first glance, but we already have all of the information we need to solve it. Let's go through it step by step.

With any problem, start by reading through the problem. As you're reading, consider:

**What question is the problem asking?****What information do you already have?**

Let's take a look at our problem again. What question is the problem asking? In other words, what are you trying to find out?

The rate to rent a small moving van is $30 per day, plus $0.50 per mile. Jada rented a van to drive to her new home. It took 2 days, and the van cost $360. __How many miles did she drive?__

There's only one question here. We're trying to find out **how many miles Jada drove**. Now we need to locate any information that will help us answer this question.

There are a few important things we know that will help us figure out the total mileage Jada drove:

- The van cost
**$30**per day. - In addition to paying a daily charge, Jada paid
**$0.50**per mile. - Jada had the van for
**2**days. - The total cost was
**$360**.

In algebra, you represent unknown numbers with letters called **variables**. (To learn more about variables, see our lesson on reading algebraic expressions.) You can use a variable in the place of any amount you don't know. Looking at our problem, do you see a quantity we should represent with a variable? It's often the number we're trying to find out.

The rate to rent a small moving van is $30 per day, plus $0.50 per mile. Jada rented a van to drive to her new home. It took 2 days, and the van cost $360. How many __miles__ did she drive?

Since we're trying to find the **total number of miles** Jada drove, we'll represent that amount with a variable—at least until we know it. We'll use the variable *m* for **miles**. Of course, we could use any variable, but *m* should be easy to remember.

Let's take another look at the problem, with the facts we'll use to solve it highlighted.

The rate to rent a small moving van is __$30 per day__, plus __$0.50 per mile__. Jada rented a van to drive to her new home. It took __2 days__, and __the van cost $360__. How many miles did she drive?

We know the total cost of the van, and we know that it includes a fee for the number of days, plus another fee for the number of miles. It's $30 per day, and $0.50 per mile. A simpler way to say this would be:

$30 per day plus $0.50 per mile is $360.

If you look at this sentence and the original problem, you can see that they basically say the same thing: It cost Jada $30 per day and $0.50 per mile, and her total cost was $360. The shorter version will be easier to translate into a mathematical expression.

Let's start by translating **$30 per day**. To calculate the cost of something that costs a certain amount per day, you'd **multiply** the per-day cost by the number of days—in other words, **30 per day** could be written as 30 ⋅days, or **30 times the number of days**. (Not sure why you'd translate it this way? Check out our lesson on writing algebraic expressions.)

$30 per day and $.50 per mile is $360

$30 ⋅ day + $.50 ⋅ mile = $360

As you can see, there were a few other words we could translate into operators, so **and $.50** became + $.50, **$.50 per mile** became $.50 ⋅ mile, and **is** became =.

Next, we'll add in the numbers and variables we already know. We already know the number of days Jada drove, **2**, so we can replace that. We've also already said we'll use *m* to represent the number of miles, so we can replace that too. We should also take the dollar signs off of the money amounts to make them consistent with the other numbers.

$30 ⋅ day + $.50 ⋅ mile = $360

30 ⋅ 2 + .5 ⋅ m = 360

Now we have our expression. All that's left to do is solve it.

This problem will take a few steps to solve. (If you're not sure how to do the math in this section, you might want to review our lesson on simplifying expressions.) First, let's simplify the expression as much as possible. We can multiply 30 and 2, so let's go ahead and do that. We can also write .5 ⋅ *m* as 0.5*m*.

30 ⋅ 2 + .5 ⋅ m = 360

60 + .5m = 360

Next, we need to do what we can to get the *m* alone on the left side of the equals sign. Once we do that, we'll know what *m* is equal to—in other words, it will let us know the number of miles in our word problem.

We can start by getting rid of the **60** on the left side by subtracting it from **both sides**.

60 | + .5m = | 360 |

-60 | -60 |

The only thing left to get rid of is **.5**. Since it's being multiplied with *m*, we'll do the reverse and **divide** both sides of the equation with it.

.5m | = | 360 |

.5 | .5 |

**.5 m / .5 **is

To make sure we solved the problem correctly, we should check our work. To do this, we can use the answer we just got—**600**—and calculate backward to find another of the quantities in our problem. In other words, if our answer for Jada's **distance** is correct, we should be able to use it to work backward and find another value, like the total cost. Let's take another look at the problem.

The rate to rent a small moving van is $30 per day, plus $0.50 per mile. Jada rented a van to drive to her new home. It took 2 days, and the van cost $360. How many miles did she drive?

According to the problem, the van costs $30 per day and $0.50 per mile. If Jada really did drive 600 miles in 2 days, she could calculate the cost like this:

$30 per day and $0.50 per mile

30 ⋅ day + .5 ⋅ mile

30 ⋅ 2 + .5 ⋅ 600

60 + 300

360

According to our math, the van would cost $360, which is exactly what the problem says. This means our solution was correct. We're done!

While some word problems will be more complicated than others, you can use these basic steps to approach any word problem. On the next page, you can try it for yourself.