To determine whether Jordan's party plans will stay within the $600 budget, we can set up an equation based on the costs.
- The cost per guest is $15, and he plans to invite 40 guests.
- The venue charges $25 per hour for 3 hours.
We can calculate the total cost as follows:
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Cost for guests: \[ \text{Cost for guests} = 40 \text{ guests} \times 15 \text{ dollars/guest} = 600 \text{ dollars} \]
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Cost for the venue: \[ \text{Cost for venue} = 25 \text{ dollars/hour} \times 3 \text{ hours} = 75 \text{ dollars} \]
Now we add the two costs together to find the total cost: \[ \text{Total cost} = \text{Cost for guests} + \text{Cost for venue} = 600 \text{ dollars} + 75 \text{ dollars} = 675 \text{ dollars} \]
Since the total cost ($675) exceeds Jordan's budget of $600, we conclude that:
Solving an equation representing this situation proves that 40 people for exactly a 3-hour party is NOT possible within the $600 budget.
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