To determine how many tickets can be purchased with a total of $685 for a family of five, let's break down the costs involved.
- Cost of Tickets: Each ticket costs $125.
- Online Processing Fee: There is an additional $5.75 processing fee per ticket.
- Parking Fee: There is a flat parking fee of $20.
Now, let \( t \) be the number of tickets you want to buy. The total cost for \( t \) tickets can be represented as:
\[ \text{Total Cost} = \text{(Cost per ticket)} \times t + \text{(Processing fee per ticket)} \times t + \text{Parking fee} \]
Putting in the values:
\[ \text{Total Cost} = 125t + 5.75t + 20 \]
Combine the ticket costs:
\[ \text{Total Cost} = (125 + 5.75)t + 20 \] \[ = 130.75t + 20 \]
We need to determine the maximum number of tickets \( t \) such that the total cost does not exceed $685. Therefore, we can form the inequality:
\[ 130.75t + 20 \leq 685 \]
Next, we subtract 20 from both sides:
\[ 130.75t \leq 665 \]
Now, divide both sides by 130.75 to solve for \( t \):
\[ t \leq \frac{665}{130.75} \approx 5.08 \]
Since \( t \) must be a whole number (you can’t buy a fraction of a ticket), the maximum number of tickets you can purchase is 5.
Now, let's check if buying 5 tickets fits within the budget:
\[ 130.75 \times 5 + 20 = 653.75 + 20 = 673.75 \]
This total cost of $673.75 is less than $685, so yes, you can purchase the tickets.
To summarize:
The inequality you need is:
\[ 130.75t + 20 \leq 685 \]
And you can purchase up to 5 tickets.
The correct response is:
125t + 5.75t + 20 ≤ 685, and yes, you can purchase the tickets.
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