Question

A group of friends wants to go to the amusement park. They have $311.50 to spend on parking and admission. Parking is $16.75, and tickets cost $32.75 per person, including tax. Write and solve an equation which can be used to determine pp, the number of people who can go to the amusement park.

Answer 1

To find the number of people \( pp \) who can go to the amusement park, we need to account for both the parking fee and the admission tickets.

1. Start with the total amount of money they have, which is $311.50.
2. The parking fee is $16.75.
3. The cost per person for admission is $32.75.

We can express the total expenses in terms of \( pp \):
- The total cost for parking is \( 16.75 \).
- The total cost for admission for \( pp \) people is \( 32.75 \times pp \).

The equation representing the total expenses is:
\[
16.75 + 32.75 \cdot pp = 311.50
\]

Now we will solve for \( pp \):

1. Subtract the parking fee from both sides of the equation:
\[
32.75 \cdot pp = 311.50 - 16.75
\]
\[
32.75 \cdot pp = 294.75
\]

2. Now, divide both sides by 32.75 to solve for \( pp \):
\[
pp = \frac{294.75}{32.75}
\]

3. Calculate the value:
\[
pp \approx 9
\]

Thus, the number of people who can go to the amusement park is approximately \( \boxed{9} \).

To confirm, let’s check the total cost for 9 people:
- Parking: \( 16.75 \)
- Admission for 9 people: \( 32.75 \times 9 = 294.75 \)
- Total: \( 16.75 + 294.75 = 311.50 \)

Since the total cost matches the budget exactly, they can indeed take 9 people to the amusement park.