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 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.
125 t less than or equal to 685 , and yes, you can purchase the tickets.

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

Answer 1

To determine whether you can purchase tickets for your family, let's start by setting up the inequality based on the costs involved.

Let \( t \) be the number of tickets. The total cost for the tickets and the parking can be represented by the following expression:

1. The cost of the tickets is \( 125t \).
2. The online processing fee for each ticket is \( 5.75t \).
3. The parking fee is a flat \( 20 \).

The total cost for tickets and parking is given by:

\[
125t + 5.75t + 20
\]

We need this total cost to be less than or equal to the total amount of money available, which is \( 685 \):

\[
125t + 5.75t + 20 \leq 685
\]

Now, we can simplify the inequality:

\[
(125 + 5.75)t + 20 \leq 685
\]

\[
130.75t + 20 \leq 685
\]

Next, we'll subtract 20 from both sides:

\[
130.75t \leq 665
\]

Now, divide both sides by \( 130.75 \):

\[
t \leq \frac{665}{130.75} \approx 5.08
\]

Since you cannot purchase a fraction of a ticket, the largest whole number \( t \) you can purchase is 5 tickets. Since there are 5 family members, you will need exactly 5 tickets.

Now let's check the total cost if you were to purchase 5 tickets:

\[
\text{Total Cost} = 125(5) + 5.75(5) + 20
\]
\[
= 625 + 28.75 + 20
\]
\[
= 673.75
\]

This total cost is less than \( 685 \), confirming that you can indeed purchase the 5 tickets. Therefore, the correct response is:

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