Chapter 0.1, Problem 18E

To determine

To determine the linear equation that gives the total monthly fee $F$ of a club member who accumulates $t$ hours of court time during the month.

Answer to Problem 18E

The linear equation that gives the total monthly fee $F$ of a club member who accumulates $t$ hours of court time:

  $F\left(t\right)=65+50t$ .

Explanation of Solution

Given:

Given that the tennis club charges a monthly fee of $\$65$ and a rate of $\$25$ for each half −hour of court time.

Calculation:

Since the club charges $\$25$ for each half −hour of court time, it charges $\$2\cdot 25$ for each hour of court time.

That is, the club charges $\$50$ for each hour of court time.

Then, the charge of accumulating $t$ hours of court time:

  $\$50\cdot t$ .

Given monthly membership fee:

  $\$65$ .

Thus, the total amount charged on the member who did accumulate $t$ hours of court time:

  $\$65+50t$ .

Let $F$ be the total charge on the member who did accumulate $t$ hours of court time in dollars.

Then, it follows that:

  $F\left(t\right)=65+50t$ .

Observe that $F\left(t\right)=65+50t$ is the equation of a line with slope $50$ and $y$ -intercept $65$ .

Thus, the linear equation that gives the total monthly fee $F$ of a club member who accumulates $t$ hours of court time:

  $F\left(t\right)=65+50t$ .

Conclusion:

The linear equation that gives the total monthly fee $F$ of a club member who accumulates $t$ hours of court time:

  $F\left(t\right)=65+50t$ .