Math Help for Section 3.1, Page 108
Additional
Example
You enroll in a guitar class. There is an enrollment fee of \$35.
You pay a total of \$125 for the enrollment fee and 4 lessons. How much
did each lesson cost?
SOLUTION
| Verbal Model: |
$\boxed{\eqalign{&\text{Enrollment} \cr &\text{Fee}}}\;+\; \boxed{\eqalign{&\text{Number of} \cr &\text{lessons}}}\;\bullet\;\boxed{\eqalign{&\text{Cost per} \cr &\text{lesson}}}\;=\;\boxed{\eqalign{&\text{Total} \cr &\text{cost}}} $ |
||
| Labels: | Enrollment fee $=35$ | (dollars) | |
| Number of lessons $=4$ | (lessons) | ||
| Cost per lesson $=x$ | (dollars) | ||
| Total cost $=125$ | (dollars) | ||
| Equation: | $\eqalign{35+4x=&125}$ | ||
You can solve this equation as follows.
$\eqalign{35+4x=&125
&{\small\color{red}\quad\quad\text{Write equation.}}
\cr 4x=&90
&{\small\color{red}\quad\quad\text{Subtract 35 from each
side.}} \cr x=&22.5
&{\small\color{red}\quad\quad\text{Divide each side by 4.}}} $
So, each lesson costs \$22.50.
Checking
a Solution
Any
time you solve an equation, you should check your answer by
substituting it back into the original equation. You can check the
above solution as follows.
$\eqalign{35+4x=&125
&{\small\color{red}\quad\quad\text{Write original equation.}}
\cr 35+4({\color{red}22.5})=&125
&{\small\color{red}\quad\quad\text{Substitute 22.5 for }x.} \cr
35+90=&22.5
&{\small\color{red}\quad\quad\text{Multiply.}}
\cr125=&125
&{\small\color{red}\quad\quad\text{Solution checks.
}\checkmark}} $