A group of friends wants to go to the amusement park. They have no more than $345 to spend on parking and admission. Parking is $17.25, and tickets cost $28.75 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.
Let p be the number of people who can go to the amusement park.
The total cost for parking is given by 17.25p.
The total cost for tickets is given by 28.75p.
The total cost for parking and tickets cannot exceed 345 dollars.
Therefore, the inequality is:
17.25p + 28.75p ≤ 345.
Combining like terms, we get:
46p ≤ 345.
Dividing both sides by 46, we get:
p ≤ 7.5.
Therefore, the number of people who can go to the amusement park is less than or equal to 7.5. Since there cannot be a fraction of a person, the maximum number of people who can go to the amusement park is 7. Answer: \boxed{7}.
To determine the number of people who can go to the amusement park, we can use the following inequality:
p * 28.75 + 17.25 ≤ 345
Let's break it down:
p - represents the number of people who can go to the amusement park.
28.75 - represents the cost of tickets per person, including tax.
17.25 - represents the cost of parking.
345 - represents the maximum amount of money the group has to spend on parking and admission.
The inequality states that the sum of the cost of tickets (p * 28.75) and the cost of parking (17.25) should be less than or equal to the maximum amount they have to spend (345).
Now, let's solve the inequality to find the maximum number of people who can go to the amusement park.
p * 28.75 + 17.25 ≤ 345
p * 28.75 ≤ 345 - 17.25
p * 28.75 ≤ 327.75
p ≤ 327.75 / 28.75
p ≤ 11.38
Therefore, a group of no more than 11 people can go to the amusement park based on the given budget constraint.