To determine how many tickets you can purchase for your family of five with the available budget of $685, we will analyze the inequalities you've provided.
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Inequality for ticket costs only:
\[ 125t \leq 685 \]
Here, \( t \) represents the number of tickets.
To find the maximum number of tickets \( t \), we solve the inequality:
\[ t \leq \frac{685}{125} \approx 5.48 \]
Since \( t \) must be a whole number, you can purchase at most 5 tickets.
This does not account for the parking or processing fee, so while you can buy up to 5 tickets based on ticket cost alone, let's also explore the other inequalities.
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Inequality for ticket costs with processing fees:
\[ 125t + 5.75t \leq 685 \]
This combines the cost of tickets and the processing fee per ticket. This simplifies to:
\[ (125 + 5.75)t \leq 685 \]
\[ 130.75t \leq 685 \]
Solving for \( t \):
\[ t \leq \frac{685}{130.75} \approx 5.24 \]
Again, rounding down means you can still buy at most 5 tickets, but this doesn't consider parking charges.
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Inequality including parking costs:
\[ 125t + 5.75t + 20 \leq 685 \]
Simplifying:
\[ 130.75t + 20 \leq 685 \]
\[ 130.75t \leq 665 \]
\[ t \leq \frac{665}{130.75} \approx 5.08 \]
Again, you can afford 5 tickets, as it must be a whole number.
Finally, let's summarize:
- Based on the ticket price alone: You can buy up to 5 tickets.
- Considering the processing fees: You can still buy 5 tickets.
- Including parking: You can purchase up to 5 tickets.
Total Cost for 5 Tickets:
If you purchase 5 tickets, the total cost would be:
- Ticket costs: \( 5 \times 125 = 625 \)
- Processing fees: \( 5 \times 5.75 = 28.75 \)
- Parking: \( 20 \)
Total cost:
\[ 625 + 28.75 + 20 = 673.75 \]
Since 673.75 is within the $685 budget, yes, you can purchase the tickets. Thus, your final answer is that you can purchase 5 tickets for your family of five and still have some money leftover.
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