


Writing Equations
For some questions on the Math IIC test, you’ll need to
translate the problem from a language you’re used to—English—into
a more useful, albeit less familiar, language. We mean the language
of math, of course, and one of your main testtaking responsibilities
is to be able to write an equation based on the information given
in a problem.
You’ll also be asked to find an expression for a certain
quantity described in a word problem. The best way to learn how
to do these things quickly and effectively is to practice. Here’s
a sample problem:

To start with, you can write r + b =
50, where r is the number of red marbles and b the
number of blue marbles in the sack. This equation tell us that the
50 marbles in the sack consist entirely of red marbles and blue
marbles.
Now that you have an initial equation, you need to decipher
what exactly the question is asking for. In this problem it is clearcut:
How many blue marbles are in the sack? You must therefore find the
value of b.
Unfortunately, you need more information to do that. You
can create a second equation based on the knowledge that there are
20 more red marbles than blue marbles. This part of the word problem
can be written in the form of an equation as r = b +
20 (or b = r – 20).
Let’s list the two equations we have so far:
Using both of these equations, you can solve for b.
After a little manipulation, which we’ll cover in the coming sections,
you’ll find that b = 15 (and r =
35). Don’t worry about the solution for now—just focus on how we
translated the word problem into equations that lead to the solution.
That problem was easy. Here’s a harder one:

According to the problem, we need to find an expression
(notice, not an equation) for the price in dollars of 35 oranges.
The key to a problem like this one is working step by step. First,
find out how many of the 35 oranges aren’t free of charge.
Next, find the price of those oranges.
But wait. Did you notice that the question asked for the
price of 35 oranges in dollars? The writers of
the Math IIC are a clever bunch, if a bit sneaky. They figure that
a good number of testtakers will see only the word price and
not notice what units are asked for. Be careful not to fall into
their carefully laid trap.
We know there are 100 cents per dollar, so we can easily
convert the price by dividing by 100.
Before we move to another problem, note that the variable r didn’t
appear anywhere in the answer. Egad! It is yet another attempt (and
a common one at that) by those devious test writers to lower your
score. You may come across many problems, especially word problems,
in which extraneous information is provided only to confuse you.
Just because a variable or number appears in a problem doesn’t mean
that it will be useful in finding the answer.
Here’s another problem:

This word problem is long and complicated, but you need
to carry out just four steps to solve it:

Gus must buy
^{x} /_{y} cans of paint to cover his house.  This
will cost him
^{xp} /_{y} dollars.  The jeans Gus buys cost 10d dollars.
 Thus,
the difference, in dollars, between the cost of the paint and the
cost of the jeans is
^{ xp} /_{y} – 10d.
For the rest of this chapter, we’ll constantly be converting
word problems into equations. If you’re still uncomfortable doing
this, don’t worry. You’ll get a lot more practice in the sections
to come.
