To rent a certain meeting room, a college charges a reservation fee of $$ \$ 33 $$ and an additional fee of $$ \$ 7.30 $$ per hour. The chemistry club wants to spend at most $$ \$ 62.20 $$ 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 $$ t $$.

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To determine the possible number of hours $$ t $$ that the chemistry club can rent the meeting room without exceeding their budget of \$62.20, we can set up and solve an inequality based on the costs provided.

**Step 1: Set Up the Inequality**

The total cost to rent the meeting room consists of:
- A fixed reservation fee of \$33.
- An additional fee of \$7.30 per hour.

So, the total cost $$ C $$ for renting the room for $$ t $$ hours can be expressed as:
$$
C = 33 + 7.30t
$$

The club wants this total cost to be at most \$62.20:
$$
33 + 7.30t \leq 62.20
$$

**Step 2: Solve for $$ t $$**

1. **Subtract the reservation fee from both sides:**
   $$
   7.30t \leq 62.20 - 33
   $$
   $$
   7.30t \leq 29.20
   $$

2. **Divide both sides by the hourly rate (\$7.30) to solve for $$ t $$:**
   $$
   t \leq \frac{29.20}{7.30}
   $$
   $$
   t \leq 4
   $$

**Conclusion:**

The chemistry club can rent the meeting room for **up to 4 hours** without exceeding their budget of \$62.20. Therefore, the possible amounts of time $$ t $$ for which they could rent the meeting room are:

$$
t \leq 4 \text{ hours}
$$
The chemistry club can rent the meeting room for up to 4 hours without exceeding their budget of \$62.20.

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