To determine whether Alice can stay within the $800 budget for 30 people attending a picnic for 4 hours, we can calculate the total costs as follows:
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Entrance Cost: The park charges $20 per person. For 30 people: \[ \text{Entrance Cost} = 30 \text{ people} \times 20 \text{ dollars/person} = 600 \text{ dollars} \]
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Pavilion Cost: The park charges $50 per hour. For 4 hours: \[ \text{Pavilion Cost} = 4 \text{ hours} \times 50 \text{ dollars/hour} = 200 \text{ dollars} \]
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Total Cost: The total cost of the picnic will be the sum of the entrance cost and the pavilion cost: \[ \text{Total Cost} = \text{Entrance Cost} + \text{Pavilion Cost} = 600 \text{ dollars} + 200 \text{ dollars} = 800 \text{ dollars} \]
Now we can compare the total cost against the budget: \[ \text{Total Cost} = 800 \text{ dollars} \quad \text{(which is equal to the budget)} \]
Therefore, Alice will stay within the budget with her plans for 30 people for a 4-hour picnic.
The correct response is: Solving an equation representing this situation proves that 30 people for exactly a 4-hour picnic is possible within the $800 budget.