Let's analyze the given situation step by step.
- Calculate the total cost for tickets and parking:
- Let \( t \) be the number of tickets you want to purchase.
- The cost of one ticket is $125, and the processing fee for one ticket is $5.75.
- The parking fee is $20.
- Therefore, the total cost for \( t \) tickets is:
\[ \text{Total Cost} = (125 + 5.75)t + 20 \]
This simplifies to:
\[ \text{Total Cost} = (130.75)t + 20 \]
- Set up the inequality:
- You want to determine whether you have enough money to buy the tickets, so we set up the inequality:
\[ (130.75)t + 20 \leq 685 \]
- Solve the inequality:
- First, subtract the parking fee from both sides:
\[ (130.75)t \leq 685 - 20 \]
\[ (130.75)t \leq 665 \]
- Now, divide both sides by 130.75 to solve for \( t \):
\[ t \leq \frac{665}{130.75} \approx 5.08 \]
Since you can't buy a fraction of a ticket, you can purchase at most 5 tickets.
- Conclusion:
- You can purchase up to 5 tickets, which fits within the total budget when considering the costs. However, let's double-check by calculating the exact cost for 5 tickets:
\[ \text{Total Cost for 5 tickets} = (130.75 \cdot 5) + 20 = 653.75 + 20 = 673.75 \]
Since $673.75 is less than $685, you can indeed purchase the tickets.
Final Answer:
You can purchase 5 tickets based on the inequality \( 130.75t + 20 \leq 685 \).
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