To determine how many tickets you can purchase, let's set up the inequality based on the costs involved.
- Cost of tickets: The cost per ticket is $125.
- Processing fee per ticket: The processing fee is $5.75 per ticket.
- Parking fee: There is a flat parking fee of $20.
If \( t \) represents the number of tickets, the total cost can be expressed as: \[ \text{Total Cost} = (125 + 5.75)t + 20 \] \[ \text{Total Cost} = 130.75t + 20 \]
Now we want this total cost to be less than or equal to the total amount of money you have, which is $685. Therefore, we can set up the following inequality: \[ 130.75t + 20 \leq 685 \]
Now, let's solve this inequality step by step:
-
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 (as you can't buy a fraction of a ticket), the largest whole number value for \( t \) is 5.
Now, let’s see if you can afford 5 tickets:
- Cost for 5 tickets: \[ \text{Total Cost} = 130.75 \times 5 + 20 \] \[ = 653.75 + 20 \] \[ = 673.75 \]
Since $673.75 is less than $685, you can purchase 5 tickets.
Now, let's check the provided response options:
- \( 125t + 5.75t + 20 \leq 685 \) is correct as the inequality.
- Since the total cost with 5 tickets ($673.75) is less than $685, the final conclusion is yes, you can purchase the tickets.
Thus, the final correct choice is: 125t+5.75t+20≤685, and yes, you can purchase the tickets.
1 answer