Question

to rent a certain meeting room, a college charges a reservation fee of $39 and an additional fee of $6.90 per hour. the chemistry club wants to spend less than $66.60 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: Set up the inequality

Let \( t \) be the number of hours. The total cost is the reservation fee plus the hourly fee times the number of hours. The reservation fee is \( 39 \) and the hourly fee is \( 6.90 \). The chemistry club wants to spend less than \( 66.60 \). So the inequality is \( 39 + 6.90t<66.60 \).

Step2: Solve the inequality for \( t \)

Subtract \( 39 \) from both sides:
\( 6.90t<66.60 - 39 \)
\( 6.90t<27.60 \)
Divide both sides by \( 6.90 \):
\( t < \frac{27.60}{6.90}\)
\( t<4 \)

Since \( t \) represents the number of hours and \( t>0 \) (you can't rent for a non - positive number of hours), the possible values of \( t \) satisfy \( 0 < t < 4 \)

Answer:

The possible amounts of time \( t \) (in hours) for which they could rent the meeting room satisfy the inequality \( 0 < t < 4 \)