Answer
See below.
Work Step by Step
(a)
Consider the provided statement “A car rental agency charges 180 dollars per week plus 0.25 dollars per mile to rent a car.”
Thus, to express the weekly cost to rent the car, a linear function representing the weekly cost of renting a car will be of the form $f\left( x \right)=mx+b$.
Suppose that traveling x miles will cost an equal amount in total for renting a car from the agency per week.
Therefore, the agency that charges 180 dollars per week plus 0.25 dollars per mile fee will cost after traveling x miles and a week, $180+\left( 0.25 \right)x$.
Thus, by the above given conditions
$f\left( x \right)=180+\left( 0.25 \right)x$
Hence, to express the weekly cost to rent a car:
$f\left( x \right)=180+\left( 0.25 \right)x$.
(b)
Consider the provided statement “The weekly cost to rent the car was 395 dollars and the car rental agency charges 180 dollars per week plus 0.25 dollars per mile to rent a car.”
Thus, to calculate the number of miles driven during the week, use the linear function representing the weekly cost of renting a car of the form $f\left( x \right)=180+\left( 0.25 \right)x$ from part (a).
The weekly cost to rent the car was 395 dollars.
Therefore, from the above given condition.
$\begin{align}
& f\left( x \right)=180+\left( 0.25 \right)x \\
& 395=180+0.25x \\
& 215=0.25x \\
& \frac{215}{0.25}=x
\end{align}$
Further simplify,
$\begin{align}
& x=\frac{215}{0.25} \\
& =860
\end{align}$
Hence, the miles driven during the week were $860\text{ miles}$.
