Answer
The monthly cost for each option is $\$35$ if the bus is used $28\text{ times}$ in a month.
Work Step by Step
Consider the provided statement “The bus fare in a city is $\$1.25$. People who use the bus have the option of purchasing a monthly discount pass for $\$21.00$; with the discount pass, the fare is reduced to $\$0.50$.”
Thus, to calculate the monthly cost for each option, use the linear function representing the monthly cost to use the bus with a discount pass of the form $g\left( x \right)=21+0.5x$ from part (b), and the monthly cost to use the bus without a discount pass of the form $f\left( x \right)=1.25x$ from part (a); then set them equal.
$\begin{align}
& 1.25x=21+0.5x \\
& 0.75x=21 \\
& x=\frac{21}{0.45} \\
& =28
\end{align}$
Using a graphing calculator, we get the value of the monthly cost with the discount pass $g\left( x \right)=35$.
Therefore, the monthly cost is $\$35$ for both options if the bus is used 28 times.
