Before you can construct and solve equations
that model real world applications, you need to be able to decide which quantities
are most relevant to the problem at hand.
More specifically, as you read through
the original problem statement, it's a good idea to make a list of the quantities
that fall into the following categories:
You can keep track of the known values by using number
values that stay fixed throughout the problem
You can keep track of the unknown values by using
variables. Whenever possible, you should try to
name all
variable quantities in terms of a single variable.
For example,
consider the following problem.
A bookstore sells a certain cookbook in both hardcover and paperback editions. The hardcover edition sells for $12.95 while the paperback edition
sells for $8.95. The store sells a total of
32 cookbooks and takes in $334.40. How many paperback cookbooks are sold?
known
values
- hardcover price
= $12.95
- paperback price
= $8.95
- total cookbook
sales = $334.40
- total number
of books sold = 32
unknown
values
- # of paperback
cookbooks sold = "x"
- # of hardcover
cookbooks sold = "32 - x"
Note: Since
we know that a total of 32 cookbooks are sold, we can subtract the number
of paperbacks ("x") from this total, thereby expressing both unknown quantites
in terms of the same variable.