Question

A group of friends wants to go to the amusement park, they have 152.75 to spend on parking admission. Parking is $10.25 and tickets cost $14.25 per person, including tax. Write and solve an equation which can be used to determine. The number of people who can go to the amusement park.

Answer 1

To solve this problem, we need to set up an equation based on the total amount of money the group has, which is \( 152.75 \).

Let's define \( x \) as the number of people who will go to the amusement park.

The costs involved are:
- Parking: \( 10.25 \)
- Admission tickets: \( 14.25 \) per person

The total cost for \( x \) people, including parking, can be expressed as:
\[
\text{Total Cost} = \text{Parking Cost} + \text{Admission Cost} = 10.25 + 14.25x
\]

We know that the total spending should equal to the amount they have:
\[
10.25 + 14.25x = 152.75
\]

Now, we can solve for \( x \):
1. Subtract \( 10.25 \) from both sides:
\[
14.25x = 152.75 - 10.25
\]
\[
14.25x = 142.50
\]

2. Now divide both sides by \( 14.25 \) to solve for \( x \):
\[
x = \frac{142.50}{14.25}
\]
\[
x = 10
\]

Thus, the number of people who can go to the amusement park is \( \boxed{10} \).

Answer 2

Okay so what would the full equation be in one line?

Answer 3

The full equation in one line that represents the situation is:

\[
10.25 + 14.25x = 152.75
\]

where \( x \) is the number of people going to the amusement park.