A group of friends wants to go to the amusement park. They have no more than $210 to spend on parking and admission. Parking is $5.75, and tickets cost $29.75 per person, including tax. Which inequality can be used to determine x*x*, the maximum number of people who can go to the amusement park?

Let's break down the problem:

- **Total budget**: No more than $210.
- **Parking cost**: $5.75 (a fixed cost regardless of the number of people).
- **Ticket cost per person**: $29.75 per person.
- **Number of people**: $ x $ (this is what we need to find).

### Step 1: Express the total cost
The total cost for $ x $ people includes the parking cost and the admission cost for each person. So the total cost is:

\[
\text{Total cost} = 5.75 + 29.75 \times x
\]

### Step 2: Set up the inequality
The total cost cannot exceed $210, so the inequality that represents the situation is:

\[
5.75 + 29.75x \leq 210
\]

### Step 3: Simplify the inequality
Now, subtract $5.75 from both sides:

\[
29.75x \leq 210 - 5.75
\]

\[
29.75x \leq 204.25
\]

Finally, divide both sides by 29.75:

\[
x \leq \frac{204.25}{29.75}
\]

\[
x \leq 6.86
\]

Since $ x $ represents the number of people and must be a whole number, the maximum number of people who can go is **6**.

### Conclusion:
The inequality that can be used to determine the maximum number of people who can go to the amusement park is:

\[
5.75 + 29.75x \leq 210
\]

Do you need further details or clarification on any part of the solution?

Here are 5 related questions for further practice:
1. If the parking cost was $8 instead of $5.75, how would that change the inequality?
2. What if the friends had $250 to spend? What would the maximum number of people be?
3. If two cars are needed for parking, doubling the parking fee, how does that affect the inequality?
4. If one friend gets a discount of $5 on the ticket, how would that alter the inequality?
5. What if an additional cost of $2.50 per person for food is added? How would you adjust the inequality?

**Tip**: When solving inequalities involving multiple costs, break down each component (fixed and variable costs) to ensure clarity.

A group of friends wants to go to the amusement park. They have no more than $210 to spend on parking and admission. Parking is $5.75, and tickets cost $29.75 per person, including tax. Which inequality can be used to determine x, the maximum number of people who can go to the amusement park?

Learn how to set up and solve an inequality to find the maximum number of people who can attend an amusement park under a $210 budget. This problem involves calculating costs for parking and tickets, using the inequality 5.75 + 29.75x ≤ 210. Suitable for students in Grades 6-8.

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