A group of friends wants to go to the amusement park. They have no more than $325 to spend on parking and admission. Parking is $13, and tickets cost $39 per person, including tax. Write and solve an inequality which can be used to determine pp, the number of people who can go to the amusement park.

To solve this problem, we need to create an inequality that accounts for the total amount the group of friends can spend, which is no more than $325, while including the cost of parking and tickets.

Let:
- $ p $ represent the number of people going to the amusement park.
- Parking costs $13.
- Each ticket costs $39 per person.

### Step 1: Set up the inequality

The total cost of the trip includes two parts:
1. The fixed parking cost of $13.
2. The variable ticket cost, which is $39 per person. So, the total ticket cost is $ 39p $, where $ p $ is the number of people.

The total cost must not exceed $325. Therefore, the inequality is:

\[
13 + 39p \leq 325
\]

### Step 2: Solve the inequality

To solve for $ p $:

1. Subtract 13 from both sides:
\[
39p \leq 325 - 13
\]
\[
39p \leq 312
\]

2. Divide both sides by 39:
\[
p \leq \frac{312}{39}
\]
\[
p \leq 8
\]

### Conclusion:
The number of people, $ p $, who can go to the amusement park is at most 8.

Would you like more details or have any questions about this solution?

Here are 5 related questions to expand on the topic:
1. What happens if parking costs increase to $15?
2. How would the inequality change if the group had $400 instead of $325?
3. If the ticket price changes to $45 per person, how many people can now attend?
4. How much extra money will the group have left if exactly 6 people go?
5. What if each person also wants to spend $20 on food? How would the inequality change?

**Tip:** When dealing with cost constraints, always break down fixed and variable costs to set up your inequality clearly.

A group of friends wants to go to the amusement park. They have no more than $325 to spend on parking and admission. Parking is $13, and tickets cost $39 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 set up and solve the inequality 13 + 39p ≤ 325 to determine how many people can attend an amusement park given a $325 budget, $13 parking fee, and $39 ticket cost per person. This solution breaks down fixed and variable costs, suitable for students in Grades 6-8.

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