To determine how many tickets can be purchased with a total of $685, let's set up an inequality based on the total cost of the tickets, processing fees, and parking.
Let \( t \) be the number of tickets purchased. The total cost includes:
- The cost of the tickets: \( 125t \)
- The processing fee per ticket: \( 5.75t \)
- The parking fee: \( 20 \)
The total cost can be expressed as: \[ 125t + 5.75t + 20 \]
We want this total to be less than or equal to $685, so we can set up the inequality: \[ 125t + 5.75t + 20 \leq 685 \]
Now, combine the terms related to \( t \): \[ (125 + 5.75)t + 20 \leq 685 \] \[ 130.75t + 20 \leq 685 \]
Next, subtract 20 from both sides: \[ 130.75t \leq 665 \]
Now, divide by 130.75 to solve for \( t \): \[ t \leq \frac{665}{130.75} \] \[ t \leq 5.08 \]
Since \( t \) must be a whole number (as you can't buy a fraction of a ticket), this means the maximum number of tickets that can be bought is \( t = 5 \).
Now, let's calculate the total cost for 5 tickets to confirm we can afford it: \[ \text{Cost for 5 tickets} = 125 \times 5 + 5.75 \times 5 + 20 \] \[ = 625 + 28.75 + 20 \] \[ = 673.75 \]
Since 673.75 is less than 685, we can indeed buy the tickets.
Thus, the correct response is: 125t + 5.75t + 20 ≤ 685, and yes, you can purchase the tickets.