Question

to rent a certain meeting room, a college charges a reservation fee of $44 and an additional fee of $7.30 per hour. the film club wants to spend at most $95.10 on renting the meeting room. what are the possible amounts of time for which they could rent the meeting room? use t for the number of hours the meeting room is rented, and solve your inequality for t.

Explanation:

Step1: Define the cost function

The total cost to rent the room is the reservation fee plus the hourly fee times the number of hours. So the cost \( C = 44 + 7.30t \). Since they want to spend at most \( \$95.10 \), we have the inequality \( 44 + 7.30t \leq 95.10 \).

Step2: Subtract 44 from both sides

Subtract 44 from each side of the inequality: \( 7.30t \leq 95.10 - 44 \). Calculating the right side, \( 95.10 - 44 = 51.10 \), so \( 7.30t \leq 51.10 \).

Step3: Divide by 7.30

Divide both sides by 7.30 to solve for \( t \): \( t \leq \frac{51.10}{7.30} \). Calculating the division, \( \frac{51.10}{7.30}=7 \), so \( t \leq 7 \). Also, since time can't be negative, \( t\geq0 \), so the possible times are \( 0\leq t\leq7 \) (or \( t \) is between 0 and 7 hours, inclusive). But following the problem's request to solve the inequality for \( t \) from the setup, the main inequality solution is \( t \leq 7 \) with \( t\geq0 \), but the inequality from the steps is \( 44 + 7.30t \leq 95.10 \) leading to \( t \leq 7 \).

Answer:

The inequality is \( 44 + 7.30t \leq 95.10 \) and solving gives \( t \leq 7 \) (with \( t\geq0 \) as a practical constraint, but the solved inequality for \( t \) is \( t \leq 7 \)). So the possible time \( t \) satisfies \( t \leq 7 \) (and \( t\geq0 \), so \( 0\leq t\leq7 \) hours).