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.
125 t plus 5.75 t plus 20 less than or equal to 685 , and yes, you can purchase the tickets.

1 answer

To determine how many tickets can be purchased with a total of $685, let's set up an inequality based on the total cost of the tickets, processing fees, and parking.

Let \( t \) be the number of tickets purchased. The total cost includes:

  • The cost of the tickets: \( 125t \)
  • The processing fee per ticket: \( 5.75t \)
  • The parking fee: \( 20 \)

The total cost can be expressed as: \[ 125t + 5.75t + 20 \]

We want this total to be less than or equal to $685, so we can set up the inequality: \[ 125t + 5.75t + 20 \leq 685 \]

Now, combine the terms related to \( t \): \[ (125 + 5.75)t + 20 \leq 685 \] \[ 130.75t + 20 \leq 685 \]

Next, subtract 20 from both sides: \[ 130.75t \leq 665 \]

Now, divide by 130.75 to solve for \( t \): \[ t \leq \frac{665}{130.75} \] \[ t \leq 5.08 \]

Since \( t \) must be a whole number (as you can't buy a fraction of a ticket), this means the maximum number of tickets that can be bought is \( t = 5 \).

Now, let's calculate the total cost for 5 tickets to confirm we can afford it: \[ \text{Cost for 5 tickets} = 125 \times 5 + 5.75 \times 5 + 20 \] \[ = 625 + 28.75 + 20 \] \[ = 673.75 \]

Since 673.75 is less than 685, we can indeed buy the tickets.

Thus, the correct response is: 125t + 5.75t + 20 ≤ 685, and yes, you can purchase the tickets.