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≤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≤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+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.

1 answer

To determine how many tickets your family can purchase, we can set up the following inequality.

Let \( t \) represent the number of tickets you want to buy. The total cost for the tickets includes:

  • the cost of the tickets, which is $125 per ticket, so that’s \( 125t \);
  • the online processing fee of $5.75 per ticket, which adds \( 5.75t \);
  • and the parking fee of $20.

The total amount spent can be represented as: \[ 125t + 5.75t + 20 \]

You want this total to be less than or equal to the amount of money you have, which is $685:

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

Combining like terms gives:

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

This simplifies to:

\[ 130.75t + 20 \leq 685 \]

Next, subtract 20 from both sides:

\[ 130.75t \leq 665 \]

Now, divide both sides by 130.75 to solve for \( t \):

\[ t \leq \frac{665}{130.75} \approx 5.09 \]

Since you can't purchase a fraction of a ticket, you can buy at most 5 tickets.

Now, let's check if you can afford 5 tickets:

  1. Cost of tickets: \( 125 \times 5 = 625 \)
  2. Processing fees: \( 5.75 \times 5 = 28.75 \)
  3. Parking fee: $20

Total Cost: \[ 625 + 28.75 + 20 = 673.75 \]

Since $673.75 is less than $685, you do have enough money.

Thus, the correct response is:

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