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.(1 point)
Responses

125t+5.75t+20≤685

, and yes, you can purchase the tickets.
125 t plus 5.75 t plus 20 less than or equal to 685 , and yes, you can purchase the tickets.
125t+5.75t+20≤685
, and no, you cannot purchase the tickets.
125 t plus 5.75 t plus 20 less than or equal to 685 , and no, you cannot purchase the tickets.
125t+5.75t≤685
, and yes, you can purchase the tickets.
125 t plus 5.75 t less than or equal to 685 , and yes, you can purchase the tickets.
125t≤685
, and yes, you can purchase the tickets.

Answer 1

To determine if you can afford tickets for your family of five, let's first create the inequality based on the costs associated with buying the tickets.

1. Let \( t \) represent the number of tickets.
2. The cost for each ticket is $125, and the online processing fee is $5.75 per ticket.
3. You also need to account for the parking fee of $20.

The total cost for \( t \) tickets can be calculated as follows:

\[
\text{Total Cost} = (\text{Cost of Tickets}) + (\text{Processing Fees}) + (\text{Parking Fee})
\]
\[
\text{Total Cost} = (125t) + (5.75t) + 20
\]

Now we can combine the terms:

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

Now we will set up the inequality:

\[
130.75t + 20 \leq 685
\]

Next, we will solve this inequality to find out how many tickets can be purchased:

1. Subtract 20 from both sides:
\[
130.75t \leq 685 - 20
\]
\[
130.75t \leq 665
\]

2. Divide both sides by 130.75 to isolate \( t \):
\[
t \leq \frac{665}{130.75}
\]
\[
t \leq 5.08
\]

Since you cannot buy a fraction of a ticket, you can buy at most 5 tickets.

Now we summarize the results:

- The inequality is \( 130.75t + 20 \leq 685 \).
- Based on this inequality, you can purchase **5 tickets**.

So the correct response is:
\[
125t + 5.75t + 20 \leq 685, \text{ and yes, you can purchase the tickets (5 tickets).}
\]