Question
A group of friends wants to go to the amusement park. They have $190 to spend on parking and admission. Parking is $6, and tickets cost $23 per person, including tax. Write and solve an equation which can be used to determine p, the number of people who can go to the amusement park.
Answers
GPT-4o mini
To determine the number of people \( p \) who can go to the amusement park given the budget of $190 for parking and admission, we can set up an equation based on the costs involved.
1. First, we account for the parking cost, which is $6.
2. Next, we calculate the cost for \( p \) tickets, where each ticket costs $23.
The total cost can be expressed as:
\[
\text{Total Cost} = \text{Parking Cost} + \text{Cost of Tickets}
\]
\[
\text{Total Cost} = 6 + 23p
\]
Since the total cost cannot exceed the budget of $190, we can set up the following inequality:
\[
6 + 23p \leq 190
\]
Next, we can solve for \( p \):
1. Subtract 6 from both sides:
\[
23p \leq 190 - 6
\]
\[
23p \leq 184
\]
2. Divide both sides by 23:
\[
p \leq \frac{184}{23}
\]
\[
p \leq 8
\]
Thus, the maximum number of people \( p \) who can go to the amusement park is 8.
1. First, we account for the parking cost, which is $6.
2. Next, we calculate the cost for \( p \) tickets, where each ticket costs $23.
The total cost can be expressed as:
\[
\text{Total Cost} = \text{Parking Cost} + \text{Cost of Tickets}
\]
\[
\text{Total Cost} = 6 + 23p
\]
Since the total cost cannot exceed the budget of $190, we can set up the following inequality:
\[
6 + 23p \leq 190
\]
Next, we can solve for \( p \):
1. Subtract 6 from both sides:
\[
23p \leq 190 - 6
\]
\[
23p \leq 184
\]
2. Divide both sides by 23:
\[
p \leq \frac{184}{23}
\]
\[
p \leq 8
\]
Thus, the maximum number of people \( p \) who can go to the amusement park is 8.
whats the equation
GPT-4o mini
The equation that can be used to determine \( p \), the number of people who can go to the amusement park, given a total budget of $190 for parking and admission, is:
\[
6 + 23p = 190
\]
This equation represents the total cost of parking (\$6) plus the cost of admission for \( p \) people (where each ticket costs \$23) being equal to the total budget of $190.
To find the maximum number of people that can attend, you can also consider it as an inequality:
\[
6 + 23p \leq 190
\]
Both forms of the equation are useful for determining \( p \), but the equality is specifically for when the budget is fully spent.
\[
6 + 23p = 190
\]
This equation represents the total cost of parking (\$6) plus the cost of admission for \( p \) people (where each ticket costs \$23) being equal to the total budget of $190.
To find the maximum number of people that can attend, you can also consider it as an inequality:
\[
6 + 23p \leq 190
\]
Both forms of the equation are useful for determining \( p \), but the equality is specifically for when the budget is fully spent.
what is the equation without it being simplified
GPT-4o mini
The equation without simplification, representing the total cost of parking and admission within the budget, is:
\[
6 + 23p - 190 = 0
\]
This equation is set to zero, indicating that the total cost of parking plus the cost of tickets for \( p \) people equals the total budget of $190.
\[
6 + 23p - 190 = 0
\]
This equation is set to zero, indicating that the total cost of parking plus the cost of tickets for \( p \) people equals the total budget of $190.