#
Section 1-7

#
Problem Solving Using Linear Equations

Many
word problems
can be translated into linear equations, and then solved
using the techniques discussed in this chapter.

You need to figure out which operations are being used, and what the unknowns
are. You may need to use a known formula.

**
Example:
**

The width of a rectangle is 14 cm less than the length. The perimeter is
100 cm. Find the dimensions of the rectangle.

Use the formula for
perimeter
:

**
***
P
*
= 2
*
l
*
+ 2
*
w
*

**
100 = 2
***
l
*
+ 2
*
w
*

We can write
*
w
*
in terms of
*
l
*
, so that we only have one unknown.

**
***
w
*
=
*
l
*
– 14

Now we get the equation:

**
100 = 2
***
l
*
+ 2(
*
l
*
– 14)

This can be simplified and solved in the usual way.