To solve this problem, we need to interpret the inequality based on the costs and the budget.

Given Information

1. Total Budget: $560
2. Parking Cost: $19.25 (one-time fee)
3. Ticket Cost per Person: $19.75
4. Variable $x$: The number of people who can attend the park.

Formulating the Inequality

The total cost for the group consists of the parking cost plus the cost of tickets for $x$ people. This is represented by: $19.75x + 19.25$

Since the group cannot spend more than $560, the inequality that represents this situation is: $19.75x + 19.25 \leq 560$

Choosing the Correct Option

From the answer choices provided, the correct inequality is: $19.75x + 19.25 \leq 560$ This matches the choice: $560 \geq 19.75x + 19.25$

Thus, the correct answer is:

• $560 \geq 19.75x + 19.25$

Would you like further details on solving this inequality or have any other questions?

Related Questions

1. How would the inequality change if there were a discount on tickets?
2. What if the budget increased to $600? How would that affect the maximum number of people?
3. How would the inequality look if there was an additional fee for each car parked?
4. What if each person had to buy a meal costing $10? How would that impact the inequality?
5. How do we interpret the solution to an inequality graphically?

Tip

When dealing with inequalities, always double-check which side represents the total cost and ensure it stays within the specified budget.