To determine how many tickets can be purchased, we can set up an inequality based on the cost of the tickets, the processing fees, and the parking fee.
Let's denote \( t \) as the number of tickets.
The total cost for the tickets, including the processing fees and parking, can be expressed as:
\[ \text{Total Cost} = (\text{Cost of Tickets}) + (\text{Processing Fees}) + (\text{Parking Fee}) \] \[ = 125t + 5.75t + 20 \]
We want this total cost to be less than or equal to the amount of money we have, which is $685. Therefore, we can write the following inequality:
\[ 125t + 5.75t + 20 \leq 685 \]
Now we can simplify the left side:
\[ (125 + 5.75)t + 20 \leq 685 \] \[ 130.75t + 20 \leq 685 \]
Next, we will isolate \( t \) in this inequality:
- Subtract 20 from both sides:
\[ 130.75t \leq 685 - 20 \] \[ 130.75t \leq 665 \]
- Divide both sides by 130.75:
\[ t \leq \frac{665}{130.75} \approx 5.08 \]
Since \( t \) must be a whole number (you can't purchase a fraction of a ticket), we can conclude that:
\[ t \leq 5 \]
This means you can purchase a maximum of 5 tickets under the given budget.
Conclusion:
The correct option based on our analysis is: 125t + 5.75t + 20 ≤ 685, and yes, you can purchase the tickets.
You can buy exactly 5 tickets, which fits within your budget.
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