To determine if your family can afford the tickets to the theme park, we need to set up an inequality that represents the total cost based on the number of tickets \( t \) you want to buy.
The total cost of the tickets is composed of the cost per ticket, the processing fee, and the parking fee.
- Cost of tickets: \( 125t \)
- Processing fee: \( 5.75t \)
- Parking fee: \( 20 \)
Putting this all together, the total cost can be expressed as: \[ 125t + 5.75t + 20 \] This needs to be less than or equal to your total budget of $685: \[ 125t + 5.75t + 20 \leq 685 \]
Now, let's combine the terms: \[ (125 + 5.75)t + 20 \leq 685 \] \[ 130.75t + 20 \leq 685 \]
Next, we subtract 20 from both sides of the inequality: \[ 130.75t \leq 665 \]
Now, 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 buy a fraction of a ticket), you can purchase a maximum of 5 tickets.
Now we can check if this is possible:
If you buy 5 tickets:
- Ticket cost: \( 125 \times 5 = 625 \)
- Processing fee: \( 5.75 \times 5 = 28.75 \)
- Parking fee: \( 20 \)
Total cost for 5 tickets: \[ 625 + 28.75 + 20 = 673.75 \]
Since this total ($673.75) is less than your budget of $685, you can afford it.
So, to summarize, the correct choice based on the calculation is: $125t + 5.75t + 20 \leqslant 685$ and yes, you can purchase the tickets.