To determine how many tickets your family can purchase, we can set up the following inequality.
Let \( t \) represent the number of tickets you want to buy. The total cost for the tickets includes:
- the cost of the tickets, which is $125 per ticket, so that’s \( 125t \);
- the online processing fee of $5.75 per ticket, which adds \( 5.75t \);
- and the parking fee of $20.
The total amount spent can be represented as: \[ 125t + 5.75t + 20 \]
You want this total to be less than or equal to the amount of money you have, which is $685:
\[ 125t + 5.75t + 20 \leq 685 \]
Combining like terms gives:
\[ (125 + 5.75)t + 20 \leq 685 \]
This simplifies to:
\[ 130.75t + 20 \leq 685 \]
Next, subtract 20 from both sides:
\[ 130.75t \leq 665 \]
Now, divide both sides by 130.75 to solve for \( t \):
\[ t \leq \frac{665}{130.75} \approx 5.09 \]
Since you can't purchase a fraction of a ticket, you can buy at most 5 tickets.
Now, let's check if you can afford 5 tickets:
- Cost of tickets: \( 125 \times 5 = 625 \)
- Processing fees: \( 5.75 \times 5 = 28.75 \)
- Parking fee: $20
Total Cost: \[ 625 + 28.75 + 20 = 673.75 \]
Since $673.75 is less than $685, you do have enough money.
Thus, the correct response is:
125t + 5.75t + 20 ≤ 685, and yes, you can purchase the tickets.