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The problem is asking for an inequality that represents the situation where a group of friends is going to an amusement park with a budget constraint of $345. The costs include a parking fee and ticket prices for each person.

Here’s how to break it down:

### Problem details:
- **Total budget**: $345
- **Parking cost**: $17.25
- **Ticket cost per person**: $28.75
- **Let $ p $ represent the number of people going to the park.**

### Forming the inequality:
The total cost of the trip is made up of the parking fee plus the cost of tickets for each person.

The total cost is:
\[
\text{Total Cost} = \text{Parking Fee} + (\text{Ticket Price per Person} \times p)
\]
Substitute the given values:
\[
\text{Total Cost} = 17.25 + 28.75p
\]

Since the group cannot spend more than $345, the inequality is:
\[
17.25 + 28.75p \leq 345
\]

### Solving the inequality:
Now, solve for $ p $:

1. Subtract 17.25 from both sides:
   \[
   28.75p \leq 345 - 17.25
   \]
   \[
   28.75p \leq 327.75
   \]

2. Divide both sides by 28.75:
   \[
   p \leq \frac{327.75}{28.75}
   \]
   \[
   p \leq 11.4
   \]

Since $ p $ represents the number of people, and it must be a whole number, the maximum number of people that can attend is 11.

Thus, the inequality to determine how many people can go is:
\[
17.25 + 28.75p \leq 345
\]
And the solution for $ p $ is $ p \leq 11 $.

---

Would you like more details on solving inequalities or any other step? Here are some related questions:

1. How do you handle inequalities with decimals?
2. What happens if you solve an inequality with a negative number?
3. How can you graph this inequality?
4. What is the importance of the budget constraint in real-world problems?
5. How would this change if the parking fee were different?

**Tip**: Always check if the value you get for $ p $ is reasonable, especially when dealing with real-life constraints like money and people!

A group of friends wants to go to the amusement park. They have no more than $345 to spend on parking and admission. Parking is $17.25, and tickets cost $28.75 per person, including tax. Write and solve an inequality which can be used to determine p, the number of people who can go to the amusement park.

Learn how to solve a real-world inequality problem involving a group of friends going to an amusement park with a total budget of $345. The problem includes calculating total costs, forming a linear inequality, and determining the number of people who can attend based on ticket and parking prices.

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