Basic Math and Pre-Algebra For Dummies (25 page)

As I say earlier in this section, this problem is about as hard as they come at this stage of math. Copy it down and try solving it step by step with the book closed.

Chapter 6

In This Chapter

Dispelling myths about word problems

Knowing the four steps to solving a word problem

Jotting down simple word equations that condense the important information

Writing more-complex word equations

Plugging numbers into the word equations to solve the problem

Attacking more-complex word problems with confidence

The very mention of word problems — or story problems, as they're sometimes called — is enough to send a cold shiver of terror into the bones of the average math student. Many would rather swim across a moat full of hungry crocodiles than “figure out how many bushels of corn Farmer Brown picked” or “help Aunt Sylvia decide how many cookies to bake.” But word problems help you understand the logic behind setting up equations in real-life situations, making math actually useful — even if the scenarios in the word problems you practice on are pretty far-fetched.

In this chapter, I dispel a few myths about word problems. Then I show you how to solve a word problem in four simple steps. After you understand the basics, I show you how to solve more-complex problems. Some of these problems have longer numbers to calculate, and others may have more complicated stories. In either case, you can see how to work through them step by step.

Here are two common myths about word problems:

• Word problems are always hard.
  
• Word problems are only for school — after that, you don't need them.
  

Both of these ideas are untrue. But they're so common that I want to address them head-on.

Word problems don't have to be hard. For example, here's a word problem that you may have run into in first grade:

• Adam had 4 apples. Then Brenda gave him 5 more apples. How many apples does Adam have now?
  

You can probably do the math in your head, but when you were starting out in math, you may have written it down:

• 4 + 5 = 9
  

Finally, if you had one of those teachers who made you write out your answer in complete sentences, you wrote “Adam has 9 apples.” (Of course, if you were the class clown, you probably wrote, “Adam doesn't have any apples because he ate them all.”)

Word problems seem hard when they get too complex to solve in your head and you don't have a system for solving them. In this chapter, I give you a system and show you how to apply it to problems of increasing difficulty. And in Chapters
13
,
18
, and
23
, I give you further practice solving more difficult word problems.

In the real world, math rarely comes in the form of equations. It comes in the form of situations that are very similar to word problems.

Whenever you paint a room, prepare a budget, bake a double batch of oatmeal cookies, estimate the cost of a vacation, buy wood to build a shelf, do your taxes, or weigh the pros and cons of buying a car versus leasing one, you need math. And the math skill you need most is understanding how to turn the
situation
you're facing into numbers that you calculate.

Word problems give you practice turning situations — or stories — into numbers.

Generally, solving a word problem involves four steps:

1. Read through the problem and set up a
   word equation
   — that is, an equation that contains words as well as numbers.
   
2.  
   Plug in numbers in place of words wherever possible to set up a regular math equation.
   
3. Use math to solve the equation.
   
4. Answer the question the problem asks.
   

Most of this book is about Step 3. This chapter and Chapters
13
,
18
, and
23
are all about Steps 1 and 2. I show you how to break down a word problem sentence by sentence, jot down the information you need to solve the problem, and then substitute numbers for words to set up an equation.

When you know how to turn a word problem into an equation, the hard part is done. Then you can use the rest of what you find in this book to figure out how to do Step 3 — solve the equation. From there, Step 4 is usually pretty easy, though at the end of each example, I make sure you understand how to do it.

The first step to solving a word problem is reading it and putting the information you find into a useful form. In this section, I show you how to squeeze the juice out of a word problem and leave the pits behind!

Most word problems give you information about numbers, telling you exactly how much, how many, how fast, how big, and so forth. Here are some examples:

• Nunu is spinning 17 plates.
  
• The width of the house is 80 feet.
  
• If the local train is going 25 miles per hour …
  

You need this information to solve the problem. And paper is cheap, so don't be afraid to use it. (If you're concerned about trees, write on the back of all that junk mail you get.) Have a piece of scrap paper handy and jot down a few notes as you read through a word problem.

For example, here's how you can jot down “Nunu is spinning 17 plates”:

• Nunu = 17
  

Here's how to note that “the width of the house is 80 feet”:

• width = 80
  

The third example tells you, “If the local train is going 25 miles per hour... .” So you can jot down the following:

• local = 25
  

 Don't let the word
if
confuse you. When a problem says “If so-and-so were true …” and then asks you a question, assume that it
is
true and use this information to answer the question.

When you jot down information this way, you're really turning words into a more useful form called a
word equation.
A word equation has an equals sign like a math equation, but it contains both words and numbers.

When you start doing word problems, you notice that certain words and phrases show up over and over again. For example,