A telephone company charges $x$ cents for the first minute of a call and charges for any additional time at the rate of $y$ cents per minute. If a certain call costs $\$6.75$ and lasts more than one minute, which of the following expressions represents the length of that call, in minutes?
[STEP]Write the expression of cost of additional time exceeding the first minute in terms of $x$[/STEP]
The cost of additional time exceeding the first minute is $\$\left(6.75-\frac{x}{100}\right)=\$\left(\frac{675-x}{100}\right)$.
[STEP]Write the expression of the exceeding time in terms of $x$ and $y$[/STEP]
Since the additional time cost $\$\left(\frac{y}{100}\right)$ per minute, the time exceeding the first minute is
$$\frac{\text{cost}}{\text{rate}}=\frac{\frac{675-x}{100}}{\frac{y}{100}}=\frac{675-x}{y}.$$
[STEP]Including the first minute[/STEP]
We have that the total length of the call, in minutes, is
$$\frac{675-x}{y}+1=\frac{675-x+y}{y}.$$
[ANS]$\frac{675-x+y}{y}$[/ANS]
