To determine whether you can purchase tickets for your family, let's start by setting up the inequality based on the costs involved.
Let \( t \) be the number of tickets. The total cost for the tickets and the parking can be represented by the following expression:
- The cost of the tickets is \( 125t \).
- The online processing fee for each ticket is \( 5.75t \).
- The parking fee is a flat \( 20 \).
The total cost for tickets and parking is given by:
\[ 125t + 5.75t + 20 \]
We need this total cost to be less than or equal to the total amount of money available, which is \( 685 \):
\[ 125t + 5.75t + 20 \leq 685 \]
Now, we can simplify the inequality:
\[ (125 + 5.75)t + 20 \leq 685 \]
\[ 130.75t + 20 \leq 685 \]
Next, we'll subtract 20 from both sides:
\[ 130.75t \leq 665 \]
Now, divide both sides by \( 130.75 \):
\[ t \leq \frac{665}{130.75} \approx 5.08 \]
Since you cannot purchase a fraction of a ticket, the largest whole number \( t \) you can purchase is 5 tickets. Since there are 5 family members, you will need exactly 5 tickets.
Now let's check the total cost if you were to purchase 5 tickets:
\[ \text{Total Cost} = 125(5) + 5.75(5) + 20 \] \[ = 625 + 28.75 + 20 \] \[ = 673.75 \]
This total cost is less than \( 685 \), confirming that you can indeed purchase the 5 tickets. Therefore, the correct response is:
125t + 5.75t + 20 ≤ 685, and yes, you can purchase the tickets.