Final answer:
To determine the number of people who can go to the amusement park within a $150 budget, set up the inequality 13.50 + 22.75x ≤ 150, where x represents the number of people. Subtracting the parking cost and dividing by the ticket cost reveals that up to 6 people can attend without exceeding the budget.
Step-by-step explanation:
The question requires writing and solving an inequality to determine the maximum number of people who can go to an amusement park without exceeding a budget of $150, given the costs for parking and per person admission. Let's denote x as the number of people in the group.
The inequality to represent the total cost of parking and admission tickets for x people would be:
13.50 + 22.75x ≤ 150
To solve for x, follow these steps:
- Subtract the parking cost from both sides of the inequality: 22.75x ≤ 150 - 13.50
- Now simplify the right side of the inequality: 22.75x ≤ 136.50
- Finally, divide both sides by the cost per ticket to isolate x: x ≤ 136.50 / 22.75
- Simplifying further gives the maximum number of people that can be taken without exceeding the budget: x ≤ 6
Therefore, up to 6 people can go to the amusement park within the budget constraints.