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The problem involves renting a meeting room with a reservation fee of $33 and an additional hourly fee of $8.90. The film club wants to spend less than $77.50 in total. We need to find the possible number of hours, $ t $, for which the room can be rented within that budget.

### Step 1: Set up the inequality.
The total cost, $ C $, can be expressed as:
\[
C = 33 + 8.90t
\]
where $ t $ is the number of hours.

Since the film club wants to spend **less than** $77.50, we write the inequality:
\[
33 + 8.90t < 77.50
\]

### Step 2: Solve the inequality.
To isolate $ t $:

1. Subtract 33 from both sides:
\[
8.90t < 77.50 - 33
\]
\[
8.90t < 44.50
\]

2. Divide both sides by 8.90:
\[
t < \frac{44.50}{8.90}
\]
\[
t < 5
\]

### Conclusion:
The film club can rent the meeting room for less than 5 hours to stay within their budget of $77.50.

Would you like further details on any part of the solution?

Here are 5 related questions you could consider:
1. What would the maximum total cost be if they rented the room for exactly 5 hours?
2. How would the inequality change if the hourly fee increased?
3. What if the budget was $100 instead of $77.50—how many hours could they rent for?
4. How does the reservation fee impact the total cost compared to just the hourly fee?
5. What if the club wanted to spend no more than $77.50 instead of strictly less?

**Tip:** When solving inequalities, make sure to reverse the inequality sign when multiplying or dividing by negative numbers!

To rent a certain meeting room, a college charges a reservation fee of $33 and an additional fee of $8.90 per hour. The film club wants to spend less than $77.50 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.

Learn how to solve the inequality 33 + 8.90t < 77.50, representing the cost of renting a meeting room with a reservation fee and an hourly charge. This problem covers key algebra concepts and is suitable for students in Grades 7-9.

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