To determine if you can purchase tickets for your family of five with the available funds, we can create an inequality based on the costs involved.
First, let's break down the costs:
- The cost of one ticket is $125.
- The online processing fee per ticket is $5.75.
- The parking fee is $20.
If \( t \) represents the number of tickets, the total cost can be expressed as follows:
\[ \text{Total Cost} = (\text{Cost of Tickets}) + (\text{Processing Fees}) + (\text{Parking Fee}) \]
This can be formulated as:
\[ \text{Total Cost} = 125t + 5.75t + 20 \]
Now, we want to find the maximum number of tickets \( t \) that can be purchased with the total funds of $685. Therefore, we set up the inequality:
\[ 125t + 5.75t + 20 \leq 685 \]
Combining the terms gives:
\[ (125 + 5.75)t + 20 \leq 685 \]
Calculating \( 125 + 5.75 \):
\[ 130.75t + 20 \leq 685 \]
Now, subtract 20 from both sides:
\[ 130.75t \leq 665 \]
Next, divide both sides by 130.75 to isolate \( t \):
\[ t \leq \frac{665}{130.75} \approx 5.08 \]
Since \( t \) must be a whole number (you can't purchase a fraction of a ticket), the maximum number of tickets that can be purchased is 5.
Now, let's summarize our findings:
- The inequality is \( 125t + 5.75t + 20 \leq 685 \), and you can purchase up to 5 tickets.
So, the correct response is:
\( 125t + 5.75t + 20 \leq 685 \), and yes, you can purchase the tickets.