hey have no more than $205 to spend on parking and admission. Parking is $7.50, and tickets cost $32 per person, including tax. What is the maximum number of people who can go to the amusement park?

To solve this problem, we need to determine the maximum number of people that can go to the amusement park without exceeding the total budget of $205.

### Step 1: Identify the costs.
- **Parking cost**: $7.50
- **Ticket cost per person**: $32

### Step 2: Set up the inequality.
Let $ n $ be the number of people going to the amusement park.

The total cost is composed of the parking cost plus the ticket cost for $ n $ people:

\[
\text{Total Cost} = 7.50 + 32n
\]

The total cost must be less than or equal to $205:

\[
7.50 + 32n \leq 205
\]

### Step 3: Solve the inequality.
Subtract $7.50 from both sides to isolate the term involving $ n $:

\[
32n \leq 205 - 7.50
\]

\[
32n \leq 197.50
\]

Next, divide both sides by 32:

\[
n \leq \frac{197.50}{32} \approx 6.17
\]

Since $ n $ must be a whole number, we round down to the nearest whole number:

\[
n = 6
\]

### Conclusion
The maximum number of people who can go to the amusement park without exceeding the $205 budget is **6**.

Would you like more details on this solution, or do you have any questions?

Here are 5 related questions:
1. What if the ticket price increased to $35 per person? How many people could go?
2. If there was a discount on parking, reducing it to $5, how would that affect the number of people who can go?
3. How much money would be left over if 5 people went instead of 6?
4. What if you had a budget of $250 instead of $205?
5. If one person had a coupon for a free ticket, how many people could go within the $205 budget?

**Tip:** When working with inequalities, remember that dividing or multiplying both sides by a positive number keeps the inequality direction the same.

Discover how to maximize amusement park attendance within a $205 budget. Learn the steps to solve the problem involving parking costs and ticket expenses per person. Suitable for students in Grades 6-8.

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