Question
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.
Answers
GPT-4o mini
To determine if you have enough money to purchase tickets for your family of five, we'll start by calculating the total cost per ticket, including the processing fee.
1. **Calculate the total cost per ticket:**
- Ticket price: $125
- Processing fee: $5.75
- Total cost per ticket = Ticket price + Processing fee
\[
\text{Total cost per ticket} = 125 + 5.75 = 130.75
\]
2. **Calculate the cost for purchasing \( x \) tickets:**
- Let's denote the number of tickets as \( x \).
- Total cost for \( x \) tickets = Cost per ticket × Number of tickets + Parking fee
\[
\text{Total Cost} = 130.75x + 20
\]
3. **Set up the inequality:**
- You want the total cost to be less than or equal to the amount of money you have, which is $685.
\[
130.75x + 20 \leq 685
\]
4. **Solve the inequality for \( x \):**
\[
130.75x + 20 \leq 685
\]
Subtract 20 from both sides:
\[
130.75x \leq 685 - 20
\]
\[
130.75x \leq 665
\]
Divide both sides by 130.75:
\[
x \leq \frac{665}{130.75} \approx 5.08
\]
5. **Interpret the result:**
Since \( x \) must be a whole number (you can't purchase a fraction of a ticket), the maximum number of tickets \( x \) that you can purchase is 5.
6. **Check if you can purchase 5 tickets:**
Calculate the total cost for 5 tickets:
\[
\text{Total cost for 5 tickets} = 130.75 \times 5 + 20
\]
\[
= 653.75 + 20 = 673.75
\]
Now, compare this with the amount you have:
\[
673.75 \leq 685
\]
Yes, you can purchase 5 tickets, as 673.75 is less than 685.
**Conclusion:**
You can purchase **5 tickets** for your family, and you have enough money to do so.
1. **Calculate the total cost per ticket:**
- Ticket price: $125
- Processing fee: $5.75
- Total cost per ticket = Ticket price + Processing fee
\[
\text{Total cost per ticket} = 125 + 5.75 = 130.75
\]
2. **Calculate the cost for purchasing \( x \) tickets:**
- Let's denote the number of tickets as \( x \).
- Total cost for \( x \) tickets = Cost per ticket × Number of tickets + Parking fee
\[
\text{Total Cost} = 130.75x + 20
\]
3. **Set up the inequality:**
- You want the total cost to be less than or equal to the amount of money you have, which is $685.
\[
130.75x + 20 \leq 685
\]
4. **Solve the inequality for \( x \):**
\[
130.75x + 20 \leq 685
\]
Subtract 20 from both sides:
\[
130.75x \leq 685 - 20
\]
\[
130.75x \leq 665
\]
Divide both sides by 130.75:
\[
x \leq \frac{665}{130.75} \approx 5.08
\]
5. **Interpret the result:**
Since \( x \) must be a whole number (you can't purchase a fraction of a ticket), the maximum number of tickets \( x \) that you can purchase is 5.
6. **Check if you can purchase 5 tickets:**
Calculate the total cost for 5 tickets:
\[
\text{Total cost for 5 tickets} = 130.75 \times 5 + 20
\]
\[
= 653.75 + 20 = 673.75
\]
Now, compare this with the amount you have:
\[
673.75 \leq 685
\]
Yes, you can purchase 5 tickets, as 673.75 is less than 685.
**Conclusion:**
You can purchase **5 tickets** for your family, and you have enough money to do so.