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.

Question

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

Answer 1

Let's break down the costs involved with purchasing tickets for your family day out at the amusement park:

1. Ticket price: $125 per ticket.
2. Online processing fee: $5.75 per ticket.
3. Parking fee: $20 total.

You have a total of $685 to spend.

To find out if you can buy tickets for your family of five, we first need to set up the total cost for buying \( t \) tickets, which includes both the ticket price and processing fee:

The total cost \( C \) for \( t \) tickets can be represented as:

\[ C = (125 + 5.75)t + 20 \]

Plugging in the values, the equation becomes:

\[ C = 130.75t + 20 \]

Now, we need to find the inequality to determine how many tickets can be purchased within your budget of $685:

\[ 130.75t + 20 \leq 685 \]

Now, let's solve the inequality step by step:

1. Subtract $20 from both sides:

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

2. Divide both sides by $130.75 to solve for \( t \):

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

Since \( t \) must be a whole number (you can't buy a fraction of a ticket), you can purchase at most 5 tickets.

Now to check the total cost for 5 tickets:

\[ C = 130.75(5) + 20 = 653.75 + 20 = 673.75 \]

You have:

\[ 673.75 \leq 685 \]

This means that you can afford 5 tickets with the money you have.

Conclusion

Based on the inequality \( 130.75t + 20 \leq 685 \), you have sufficient funds to purchase tickets for your family. You can buy a total of 5 tickets.

So the final answer is:

The correct inequality to determine how many tickets can be purchased is:

\[ 130.75t + 20 \leq 685 \quad \text{and yes, you can purchase 5 tickets.} \]

Answer 2

that is not one of the answers provided please try agian

Answer 3

I apologize for the oversight. Let's analyze the options provided and find the correct one based on the budget and costs.

1. Total Budget: $685
2. Cost per Ticket: $125
3. Online Processing Fee per Ticket: $5.75
4. Parking Fee: $20
5. Number of Family Members: 5 (hence \( t = 5 \))

Total Cost per Ticket:

The total cost for each ticket including the processing fee is: \[ 125 + 5.75 = 130.75 \text{ dollars} \]

Total Cost with Parking:

Including the parking fee, the total cost for \( t \) tickets is: \[ C = 130.75t + 20 \]

Inequality Setup:

To check if you can purchase the tickets, the inequality we form is: \[ 130.75t + 20 \leq 685 \]

Solve for \( t \):

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

2. Divide both sides by $130.75: \[ t \leq \frac{665}{130.75} \approx 5.08 \]

Since \( t \) must be a whole number, the maximum number of tickets you can buy is 5.

Check Total Cost for 5 Tickets:

Calculating the total for 5 tickets: \[ C = 130.75 \times 5 + 20 = 653.75 + 20 = 673.75 \] You have $685, so you can afford 5 tickets.

Evaluating the Options Given:

1. Option 1: \( 125t + 5.75t + 20 \leq 685 \) and yes, you can purchase the tickets.
2. Option 2: \( 125t + 5.75t \leq 685 \) and yes, you can purchase the tickets.
3. Option 3: \( 125t \leq 685 \) and yes, you can purchase the tickets.
4. Option 4: \( 125t + 5.75t + 20 \leq 685 \) and no, you cannot purchase the tickets.

Correct Choice:

The correct inequality, including the parking fee, given that you can indeed purchase tickets, is:

Option 1: \[ 125t + 5.75t + 20 \leq 685 \quad \text{and yes, you can purchase the tickets.} \]

This correctly represents the total cost and confirms that you can buy the tickets with your budget. Thank you for your patience!