To determine if you can afford the tickets for your family of five, let's begin by setting up the appropriate inequality.
Let \( t \) be the number of tickets you want to purchase. The total cost for \( t \) tickets includes the price of the tickets, the online processing fee for each ticket, and the parking fee.
The total cost equation is: \[ 125t + 5.75t + 20 \] The combined ticket price can be simplified as: \[ (125 + 5.75)t + 20 = 130.75t + 20 \]
Now our inequality becomes: \[ 130.75t + 20 \leq 685 \]
To solve for \( t \), we first need to isolate \( t \):
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Subtract 20 from both sides: \[ 130.75t \leq 685 - 20 \] \[ 130.75t \leq 665 \]
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Now, divide both sides by 130.75: \[ t \leq \frac{665}{130.75} \] Calculating the right side: \[ t \leq 5.08 \]
Since \( t \) must be a whole number (you can't buy a fraction of a ticket), the maximum number of tickets you can purchase is 5.
Now, let's check the calculations:
- If you buy 5 tickets: \[ 130.75 \times 5 + 20 = 653.75 + 20 = 673.75 \]
- If you buy 6 tickets: \[ 130.75 \times 6 + 20 = 784.5 + 20 = 804.5 \]
So, the total cost for 5 tickets is $673.75, which is less than $685, and the total cost for 6 tickets is $804.5, which exceeds your budget. Therefore, you can buy 5 tickets.
Thus, the answer is: A: \( 125t + 5.75t + 20 \) is less than or equal to 685, and yes, you can purchase the tickets.