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The question asks which inequality can be used to determine the maximum number of people $ x $ who can go to the amusement park, given that:

- The total budget is no more than $125.
- Parking costs $16.75.
- Tickets cost $20.25 per person (including tax).

### Set up the inequality:

The total cost is the sum of parking and the cost for $ x $ people’s tickets. That is:

\[
\text{Total Cost} = 16.75 + 20.25x
\]

Since they can spend no more than $125, the inequality is:

\[
16.75 + 20.25x \leq 125
\]

Now, we look at the answer choices. The correct inequality is:

\[
\boxed{16.75 + 20.25x \leq 125}
\]

This corresponds to the fourth option in the list.

Let me know if you have questions or need further details.

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Here are some related questions for practice:
1. How would the inequality change if the parking cost increased to $20?
2. What if the group could spend exactly $125 and not a penny more? How would you write that as an equation?
3. What is the maximum number of people who can attend the park if the cost stays as described?
4. How would you solve for $ x $ from the inequality $ 16.75 + 20.25x \leq 125 $?
5. What happens if the cost per person decreases to $18?

**Tip:** Always identify fixed and variable costs separately when setting up a budget-based inequality.

A group of friends wants to go to the amusement park. They have no more than $125 to spend on parking and admission. Parking is $16.75, and tickets cost $20.25 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 determine the maximum number of people who can go to the amusement park with a budget constraint. This problem involves setting up and solving linear inequalities based on fixed and variable costs. Suitable for students in Grades 7-9.

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