Question

A group of friends wants to go to the amusement park. They have $206 to spend on parking and admission. Parking is $11, and tickets cost $16.25 per person, including tax. Write and solve an equation which can be used to determine xx, the number of people who can go to the amusement park.

Answer 1

To find out how many people can go to the amusement park, we can set up an equation based on the total amount of money the group has, which is $206.

Let \( x \) be the number of people in the group. The total cost includes the parking fee and the admission fees for all the people.

1. The parking cost is $11.
2. The admission cost for \( x \) people is \( 16.25x \).

The total cost can be expressed as follows:

\[
\text{Total Cost} = \text{Parking Cost} + \text{Admission Cost}
\]

Putting the costs into the equation:

\[
206 = 11 + 16.25x
\]

Now, we will solve for \( x \).

1. First, subtract the parking cost from both sides:

\[
206 - 11 = 16.25x
\]

\[
195 = 16.25x
\]

2. Now, divide both sides by 16.25 to isolate \( x \):

\[
x = \frac{195}{16.25}
\]

3. Calculate the value:

\[
x \approx 12
\]

Now, since \( x \) must be a whole number (you can't have a fraction of a person), we check if 12 fits within the budget:

Calculating the total cost for 12 people:
- Admission for 12 people: \( 16.25 \times 12 = 195 \)
- Total cost including parking: \( 195 + 11 = 206 \)

Since it matches the budget of $206, the solution is valid.

Thus, the number of people who can go to the amusement park is:

\[
\boxed{12}
\]