Applications of Linear Equations

This section this textbook explains how to translate the situations described in word problems to equations and provides a variety of examples. Read the chapter and work through the problems. Some examples involved the geometric facts you have learned in Unit 2.

Example 109.

A sofa and a love seat together costs $$444$ . The sofa costs double the love seat. How much do they each cost?

Love Seat $x$	With no information about the love seat,this is our $x$
Sofa $2x$	Sofa is double the love seat, so we multiply by $2$
$S + L = 444$	Together they cost $444$ , so we add
$(x) +(2x)= 444$	Replace $S$ and $L$ with labeled values
$\underline {3x = 444}$	Parenthesis are not needed, combine like terms $x +2x$
$3 \quad \quad 3$	Divide both sides by $3$
$x = 148$	Our solution for $x$
Love Seat $148$	Replace $x$ with $148$ in the original list
Sofa $2(148)= 296$	The love seat costs $$148$ and the sofa costs $$296$ .

Be careful on problems such as these. Many students see the phrase "double" and believe that means we only have to divide the $444$ by $2$ and get $$222$ for one or both of the prices. As you can see this will not work. By clearly labeling the variables in the original list we know exactly how to set up and solve these problems.