Question

Get ready for an amusement park day of fun! You and your family want to spend the day
at a theme park. You have pooled your money together and have $685. The tickets to the
park are $125 each and there is an online processing fee of $5.75 per ticket. You also need
to pay $20 for parking. If you have a family of five, do you have enough money to purchase
these tickets? Find an inequality to determine how many tickets can be purchased. Then find
how many tickets you are able to purchase based on your inequality.

125t + 5.75t + 20 ≤ 685, and yes, you can purchase the tickets.
125t + 5.75t + 20 ≤ 685, and yes, you can purchase the tickets.

125t + 5.75t ≤ 685, and yes, you can purchase the tickets.
125t + 5.75t ≤ 685, and yes, you can purchase the tickets.

125t + 5.75t + 20 ≤ 685, and no, you cannot purchase the tickets.
125t + 5.75t + 20 ≤ 685, and no, you cannot purchase the tickets.

125t ≤ 685, and yes, you can purchase the tickets.

Answer 1

Let's break down the expenses for your theme park trip with the family:

1. **Ticket Cost**: Each ticket costs $125.
2. **Processing Fee**: Each ticket also incurs a processing fee of $5.75.
3. **Parking Fee**: There is also a parking fee of $20.

First, we define the variables:

- Let \( t \) = the number of tickets you want to purchase.

Now, let's formulate the inequality:

The total cost to purchase \( t \) tickets would be:

\[
\text{Total Cost} = (\text{Ticket Cost} + \text{Processing Fee}) \cdot t + \text{Parking Fee}
\]

\[
\text{Total Cost} = (125 + 5.75)t + 20
\]

This can be simplified to:

\[
\text{Total Cost} = 130.75t + 20
\]

Now, we need to ensure that the total cost does not exceed the amount of money you have, which is $685:

\[
130.75t + 20 \leq 685
\]

Next, we can solve the inequality to find how many tickets can be purchased:

1. Subtract 20 from both sides:

\[
130.75t \leq 685 - 20
\]
\[
130.75t \leq 665
\]

2. Now, divide both sides by 130.75:

\[
t \leq \frac{665}{130.75}
\]

Calculating the right-hand side:

\[
t \leq 5.08
\]

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 \( t = 5 \).

Now, let's check if purchasing 5 tickets is possible:

\[
\text{Total Cost} = 130.75 \cdot 5 + 20 = 653.75 + 20 = 673.75
\]

This cost is less than $685, so yes, you can buy 5 tickets!

### Conclusion

You can use the inequality:
\[
130.75t + 20 \leq 685
\]
And you can purchase a maximum of **5 tickets** based on this inequality, confirming that you have enough money.