Get ready for an amusement park day of fun you and your family want to spend the day at a theme park you have pulled the money together and have $685 the ticket 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 you have enough money to purchase these tickets finding any quality to determine how many tickets can be purchased and find how many tickets you were able to purchase based on your inequality

Answer 1

Let's break down the costs step by step to determine how many tickets you can purchase for your family of five with your budget of $685.

Costs Breakdown

1. Cost of Tickets:

   • Each ticket costs $125.
   • Online processing fee per ticket: $5.75.
   • Therefore, the total cost per ticket including the fee is: \[ 125 + 5.75 = 130.75 \text{ (total cost per ticket)} \]

2. Parking Fee:

   • The parking fee is a flat $20.

Setting Up the Inequality

You want to find out how many tickets \(x\) can be purchased within your budget of $685.

The total cost for \(x\) tickets can be expressed as: \[ \text{Total Cost} = \text{Cost of Tickets} + \text{Parking Fee} = 130.75x + 20 \]

Set this total cost less than or equal to your budget: \[ 130.75x + 20 \leq 685 \]

Solving the Inequality

Now, subtract the parking fee from both sides: \[ 130.75x \leq 685 - 20 \] \[ 130.75x \leq 665 \]

Next, divide both sides by 130.75 to find \(x\): \[ x \leq \frac{665}{130.75} \approx 5.08 \]

Since you can't purchase a fraction of a ticket, round down to the nearest whole number: \[ x \leq 5 \]

Conclusion

Since you have a family of 5, you can purchase exactly 5 tickets.

Final Cost Check

1. Cost for 5 tickets:

   • Total ticket cost: \[ 5 \times 130.75 = 653.75 \]

2. Including the parking fee: \[ 653.75 + 20 = 673.75 \]

Budget Check

You started with $685: \[ 685 - 673.75 = 11.25 \]

So, you can indeed afford 5 tickets and have $11.25 left over!