# Word Problems

### Topics

## Introduction to :

We recommend reading any word problem at least three times. By the conclusion of the third reading, you should be magically whisked away to your home in Kansas.

Read it **once**...

...to get a general idea of what's going on. Is the problem about money? Height and width? Distances? Money? Yeah, we already said money, but it's important. Can you draw a picture in the margin that helps you visualize the problem?

**Twice**...

...to translate from English into math. Read the problem carefully this time, figuring out which pieces of information are important and which ones aren't. Then ignore the unnecessary bits. This may sound a bit harsh, but they're big boys. They'll get over it.

**Three times**...

...a lady. Wait, that's not it.

...to make sure you answered the right question. To be sure, read the question one last time before drawing a box around your final answer. Even if this method of double-checking saves you only once out of every 100 times, it will help you in the long run. 1 out of 100 is better than 0 out of 100, but now we're moving into some advanced mathematics.

### Sample Problem

The local department store was having a sale. Holla! Gabe bought a pair of shoes for $21, although they would have been cheaper if he'd bought penny loafers. He also bought some shirts that were on sale for 25% off their normal retail price of $18. Gabe, always the bargain hunter, spent $75 total. How many shirts did he buy? Also, does he really think any of them will go with those shoes?

Read the problem:

**Once**...

...for a general idea of what's going on: Gabe went shopping and spent money. Sounds like an old familiar story. Time for an intervention, friends of Gabe. Preferably before he maxes out his Diner's Club card.

Now we need to figure out how many shirts he bought, so we read the problem:

**Twice**...

...to translate from English into math. Remember, we can translate a bit at a time, sort of like how Gabe pays for some of his major purchases when he has them on layaway. Sheesh, Gabe. Get a hold of yourself.

(amount Gabe spent) = (amount he spent on shoes) + (amount he spent on shirts)

We know he spent $75 total, of which $21 was spent on shoes. This gives us the equation

$75 = 21 + (amount he spent on shirts).

The problem has gotten smaller. It's depressing when that happens with cake, but great when it happens to a word problem. Now all we need to do is come up with a symbolic expression for how much Gabe spent on shirts, or the cost per shirt times the number of shirts:

(amount he spent on shirts) = (cost per shirt)(number of shirts).

Since the shirts are 25% off their normal price of $18, they cost $18 – 0.25(18) = $13.50 each. What a deal, and real polyester, too!

We need to introduce a variable for the number of shirts; *s* will do the trick nicely.

(amount he spent on shirts) = 13.50*s*

When we plug this into the earlier equation, we find that

75 = 21 + 13.5*s*

Finally, we've reduced this thing to a super-simple-looking equation! Good riddance, vestiges of language! Begone, nouns and verbs!

Things look much nicer now, right? No worrying about shirts or shoes or prices or Gabe's uncontrollable shopping addiction. For the moment, we can forget about the word problem and solve the equation. The answer is *s* = 4, by the way. In case you were interested.

**Three **times...

...to make sure we're answering the right question. We want to know how many shirts Gabe bought. Is that the answer we arrived at? We found that *s* = 4, and *s* was the number of shirts Gabe bought, so we're all done. Four new shirts for Gabe, and three of them feature a Hawaiian pattern. Gabe, if you insist on buying far more clothes than you need, can't you at least have a decent fashion sense?

When translating from English into math, some information can be ignored. We don't care that "The local department store was having a sale.'' Gabe might, but we certainly don't. We care about statements that tell us numbers, and statements that tell us what the question is. Any extraneous information has been placed there simply as a decoy. We're not going to fall for that. Wait a second...*two for one*? We'll grab our jacket and meet you there.

Some people find it helpful to underline the important pieces of information in a word problem. You're like an actor highlighting in a script the lines that are important for him to remember. Unlike an actor, however, you can always look back at the original problem if you draw a blank. Also, you don't need to wear any stage makeup.

In the problem we just did, the important bits might look something like this:

The local department store was having a sale. Gabe bought a **pair of shoes for $21** and some **shirts** that were on sale for **25% off their normal retail price of $18**. If Gabe **spent $75 total, how many shirts did he buy?**

As you practice, you'll become better at figuring out which parts of the word problem you can ignore and which parts are important.