Study Guide

Equations and Inequalities - Word Problems

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Word Problems

The art of determining how and when math can and should be applied in the real world is all about translating. It's helpful to come up with a game plan for figuring out complex word problems and translating them into Algebra-ese. (Algebrish? Algebrean? Something like that.) From there, all we have to do is solve a simple math equation. Shmoop will lay out the 7 magic steps that will make deciphering word problems an alge–breeze.

Oh, you want to know what they are? Sure, no problem. Well, word problems, but we meant no problem with—actually, nevermind. Let's take a look at those seven Shmoop steps.

Step 1: Read the Problem Thoroughly

First of all, we realize that you aren’t a fool. We aren't trying to insult your intelligence by telling you to do this, but you’d be amazed how many people get problems wrong because they don’t read carefully.

Pay attention to key pieces of information, and don’t get distracted by random fun facts that have nothing to do with solving the problem. For example, if a word problem asks you how many puppies there are total in a pet shop, don't worry about how many are brown, how many are spotted, or how many are wearing hats, and definitely ignore anything that has to do with cats.

Step 2: Identify the Unknown(s)

Once we've read the problem all the way through, we should identify what we're trying to solve for. In other words, what is the problem asking us to find?

If we're having trouble, look for key parts of the problem. Sentences that end in question marks are a big giveaway. Also look for key words such as "solve for" and "identify." Identifying the unknowns will help us set a clear goal so that we don’t get carried away.

Step 3: Write It Out

A helpful way to solve any word problem is to first write an "equation" using words. That’s right, no numbers. This is a way to map out what we'll later replace with variables and numbers. If we map out our equation first, using our language of choice, it will help us understand how to go about solving for the unknowns.

Step 4: Assign Labels

Now that we’ve listed out all of the parts of the equation in words, it's time to assign labels to each part. Labels can either be numbers or variables. Assigning labels will help us transition from words to the equation that will ultimately lead to the answer.

Sometimes it can also be helpful to list out applicable units next to each label so that we don't forget to write the final answer in the proper form (e.g., feet, grams, seconds, balloon animals, etc.).

Step 5: Turn Into Numbers

Now that everything's set up, it’s just a game of replacing words with labels. When we finish replacing, we'll see a beautiful algebraic equation. It's not just a pretty face, though; it's the key to finding our answer.

Step 6: Solve

We have an equation; now to solve it for the unknown. Don't act like you didn't see this step coming.

Step 7: Answer the Question

Believe it or not, this is the step that people forget most often. They get so excited about solving for a variable that they forget that they still need to check if that solution actually answers the question posed in the problem. This is one of the reasons why we read the problem so much in Step 1 and identify the unknowns in Step 2.

Once we've arrived at a solution, we go back and read the word problem again and write out a full answer in sentence form using the appropriate solution, including units. For example, if the question asks, "How long did the jog take," a complete answer would be, "The jog took 40 minutes." Simply scribble down "40" and you probably won't get any credit, even though you just did six steps' worth of hard work.

All of this sounds simple enough when just talking about it, but go ahead and click on the Examples button up top to see the magic in action.

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