To determine if you have enough money to purchase tickets for your family of five, we first need to establish the total cost of the tickets.
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Ticket Price and Fees: Each ticket costs $125, and there is a processing fee of $5.75 per ticket. Therefore, the total cost per ticket is: \[ \text{Cost per ticket} = \text{Ticket price} + \text{Processing fee} = 125 + 5.75 = 130.75 \]
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Parking Cost: Additionally, you need to pay $20 for parking.
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Total Costs Calculation: If \( n \) represents the number of tickets you want to purchase, then the total cost \( C \) can be expressed as: \[ C = n \times 130.75 + 20 \]
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Inequality: You want to find the maximum number of tickets you can purchase without exceeding your total amount of $685. Thus, the inequality can be set up as: \[ n \times 130.75 + 20 \leq 685 \]
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Solving the Inequality:
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First, subtract 20 from both sides: \[ n \times 130.75 \leq 685 - 20 \] \[ n \times 130.75 \leq 665 \]
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Next, divide both sides by 130.75: \[ n \leq \frac{665}{130.75} \] \[ n \leq 5.08 \]
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Since \( n \) represents the number of tickets and must be a whole number, we can conclude that: \[ n \leq 5 \]
- Conclusion: You can purchase a maximum of 5 tickets. Now let's check the total cost for clarity:
- If you buy 5 tickets: \[ \text{Total cost} = 5 \times 130.75 + 20 = 653.75 + 20 = 673.75 \] This cost is less than your total budget of $685, confirming that you have enough money.
Therefore, you can indeed purchase 5 tickets for your family day at the amusement park!
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