Basic Math and Pre-Algebra For Dummies (26 page)

• Bobo is spinning five fewer plates than Nunu.
  
• The height of a house is half as long as its width.
  
• The express train is moving three times faster than the local train.
  

You've probably seen statements such as these in word problems since you were first doing math. Statements like these look like English, but they're really math, so spotting them is important. You can represent each of these types of statements as word equations that also use Big Four operations. Look again at the first example:

• Bobo is spinning five fewer plates than Nunu.
  

You don't know the number of plates that either Bobo or Nunu is spinning. But you know that these two numbers are related.

You can express this relationship like this:

• Bobo + 5 = Nunu
  

This word equation is shorter than the statement it came from. And as you see in the next section, word equations are easy to turn into the math you need to solve the problem.

Here's another example:

• The height of a house is half as long as its width.
  

You don't know the width or height of the house, but you know that these numbers are connected.

You can express this relationship between the width and height of the house as the following word equation:

With the same type of thinking, you can express “The express train is moving three times faster than the local train” as this word equation:

 As you can see, each of the examples allows you to set up a word equation using one of the Big Four operations — adding, subtracting, multiplying, and dividing.

The end of a word problem usually contains the question you need to answer to solve the problem. You can use word equations to clarify this question so you know right from the start what you're looking for.

For example, you can write the question, “All together, how many plates are Bobo and Nunu spinning?” as

• Bobo + Nunu = ?
  

You can write the question “How tall is the house” as:

• height = ?
  

Finally, you can rephrase the question “What's the difference in speed between the express train and the local train?” in this way:

• express − local = ?
  

After you've written out a bunch of word equations, you have the facts you need in a form you can use. You can often solve the problem by plugging numbers from one word equation into another. In this section, I show you how to use the word equations you built in the last section to solve three problems.

Some problems involve simple addition or subtraction. Here's an example:

• Bobo is spinning five fewer plates than Nunu. (Bobo dropped a few.) Nunu is spinning 17 plates. All together, how many plates are Bobo and Nunu spinning?
  

Here's what you have already, just from reading the problem:

•      Nunu = 17
  
• Bobo + 5 = Nunu
  

Plugging in the information gives you the following:

• Bobo + 5 = 17
  

If you see how many plates Bobo is spinning, feel free to jump ahead. If not, here's how you rewrite the addition equation as a subtraction equation (see Chapter
4
for details):

• Bobo = 17 − 5 = 12
  

The problem wants you to find out how many plates the two clowns are spinning together. So you need to find out the following:

• Bobo + Nunu = ?
  

Just plug in the numbers, substituting 12 for Bobo and 17 for Nunu:

• 12 + 17 = 29
  

So Bobo and Nunu are spinning 29 plates.

At times, a problem notes relationships that require you to use multiplication or division. Here's an example:

• The height of a house is half as long as its width, and the width of the house is 80 feet. How tall is the house?
  

You already have a head start from what you determined earlier:

You can plug in information as follows, substituting 80 for the word
width
:

So you know that the height of the house is 40 feet.

Pay careful attention to what the question is asking. You may have to set up more than one equation. Here's an example:

• The express train is moving three times faster than the local train. If the local train is going 25 miles per hour, what's the difference in speed between the express train and the local train?
  

Here's what you have so far:

Plug in the information you need:

In this problem, the question at the end asks you to find the difference in speed between the express train and the local train. Finding the difference between two numbers is subtraction, so here's what you want to find:

• express − local = ?
  

You can get what you need to know by plugging in the information you've already found:

• 75 − 25 = 50
  

Therefore, the difference in speed between the express train and the local train is 50 miles per hour.

The skills I show you previously in “Solving Basic Word Problems” are important for solving any word problem because they streamline the process and make it simpler. What's more, you can use those same skills to find your way through more complex problems. Problems become more complex when

• The calculations become harder. (For example, instead of a dress costing $30, it costs $29.95.)
  
• The amount of information in the problem increases. (For example, instead of two clowns, you have five.)
  

Don't let problems like these scare you. In this section, I show you how to use your new problem-solving skills to solve more-difficult word problems.

A lot of problems that look tough aren't much more difficult than the problems I show you in the previous sections. For example, consider this problem:

• Aunt Effie has $732.84 hidden in her pillowcase, and Aunt Jezebel has $234.19 less than Aunt Effie has. How much money do the two women have all together?
  

One question you may have is how these women ever get any sleep with all that change clinking around under their heads. But moving on to the math, even though the numbers are larger, the principle is still the same as in problems in the earlier sections. Start reading from the beginning: “Aunt Effie has $732.84 … .” This text is just information to jot down as a simple word equation:

• Effie = $732.84
  

Continuing, you read, “Aunt Jezebel has
$234.19 less than
Aunt Effie has.” It's another statement you can write as a word equation:

• Jezebel = Effie − $234.19
  

Now you can plug in the number $732.84 where you see Aunt Effie's name in the equation:

• Jezebel = $732.84 − $234.19
  

So far, the big numbers haven't been any trouble. At this point, though, you probably need to stop to do the subtraction: