Allocating a Separate Budget

Oct 13, 2025 by windailys.com 98 views

Introduction

Planning a fun-filled day at the amusement park with friends can be an exciting experience. However, it's essential to consider the costs involved, including parking and admission fees. In this scenario, a group of friends wants to visit the amusement park but has a limited budget of $480 to spend on parking and admission. The cost of parking is $8.75, and the ticket price is $15.50 per person, including tax. In this article, we will explore the mathematical problem of determining the maximum number of friends that can visit the amusement park within the given budget.

The Problem

Let's denote the number of friends as 'n'. The total cost of parking for 'n' friends is $8.75, and the total cost of admission for 'n' friends is $15.50n. The total budget for parking and admission is $480. We can set up an inequality to represent the situation:

8.75 + 15.50n ≤ 480

Solving the Inequality

To solve the inequality, we need to isolate the variable 'n'. First, we subtract 8.75 from both sides of the inequality:

15.50n ≤ 471.25

Next, we divide both sides of the inequality by 15.50:

n ≤ 30.25

Since the number of friends cannot be a fraction, we round down to the nearest whole number:

n ≤ 30

Conclusion

Based on the calculation, the maximum number of friends that can visit the amusement park within the given budget of $480 is 30. However, this calculation assumes that the cost of parking and admission remains the same for all friends. In reality, there may be additional costs, such as food, drinks, and merchandise, that need to be considered.

Additional Costs

Let's assume that each friend will spend an additional $10 on food, drinks, and merchandise. We can add this cost to the total budget:

480 + 10n ≤ 480

However, this is not a realistic scenario, as the total budget would not be sufficient to cover the additional costs. A more realistic approach would be to allocate a separate budget for additional expenses.

Allocating a Separate Budget

Let's assume that the group wants to allocate an additional $100 for food, drinks, and merchandise. We can subtract this amount from the total budget:

480 - 100 = 380

Now, we can recalculate the maximum number of friends that can visit the amusement park within the reduced budget:

8.75 + 15.50n ≤ 380

Solving the inequality, we get:

n ≤ 23.25

Rounding down to the nearest whole number, we get:

n ≤ 23

Conclusion

Based on the revised calculation, the maximum number of friends that can visit the amusement park within the reduced budget of $380 is 23. This calculation takes into account the additional costs of food, drinks, and merchandise.

Real-World Applications

This mathematical problem has real-world applications in various scenarios, such as:

Planning a group outing to a theme park or an amusement park
Budgeting for a family vacation
Allocating resources for a team-building event

Tips for Planning a Group Outing

When planning a group outing to an amusement park, consider the following tips:

Set a realistic budget and stick to it
Allocate a separate budget for additional expenses, such as food and merchandise
Consider the cost of parking and admission fees
Plan ahead and book tickets and accommodations in advance to avoid last-minute costs

Conclusion

In conclusion, the mathematical problem of determining the maximum number of friends that can visit the amusement park within a given budget is a classic example of a linear inequality. By solving the inequality, we can determine the maximum number of friends that can visit the park within the given budget. However, it's essential to consider additional costs, such as food, drinks, and merchandise, and allocate a separate budget for these expenses. By following these tips, you can plan a fun and memorable group outing to the amusement park.

Introduction

In our previous article, we explored the mathematical problem of determining the maximum number of friends that can visit the amusement park within a given budget. We set up an inequality to represent the situation and solved it to find the maximum number of friends that can visit the park. In this article, we will answer some frequently asked questions related to this problem.

Q&A

Q: What is the maximum number of friends that can visit the amusement park within the given budget of $480?

A: The maximum number of friends that can visit the amusement park within the given budget of $480 is 30.

Q: What is the cost of parking and admission for each friend?

A: The cost of parking is $8.75, and the cost of admission is $15.50 per person, including tax.

Q: How do I calculate the maximum number of friends that can visit the amusement park within a given budget?

A: To calculate the maximum number of friends that can visit the amusement park within a given budget, you need to set up an inequality that represents the situation. The inequality is:

8.75 + 15.50n ≤ 480

where n is the number of friends.

Q: What if I want to allocate a separate budget for additional expenses, such as food and merchandise?

A: If you want to allocate a separate budget for additional expenses, you need to subtract the additional budget from the total budget. For example, if you want to allocate an additional $100 for food and merchandise, you can subtract this amount from the total budget:

480 - 100 = 380

Then, you can recalculate the maximum number of friends that can visit the amusement park within the reduced budget.

Q: What are some real-world applications of this mathematical problem?

A: This mathematical problem has real-world applications in various scenarios, such as:

Planning a group outing to a theme park or an amusement park
Budgeting for a family vacation
Allocating resources for a team-building event

Q: What are some tips for planning a group outing to an amusement park?

A: When planning a group outing to an amusement park, consider the following tips:

Set a realistic budget and stick to it
Allocate a separate budget for additional expenses, such as food and merchandise
Consider the cost of parking and admission fees
Plan ahead and book tickets and accommodations in advance to avoid last-minute costs

Q: Can I use this mathematical problem to plan a group outing to a different type of event?

A: Yes, you can use this mathematical problem to plan a group outing to a different type of event, such as a concert, a sporting event, or a festival. The key is to set up an inequality that represents the situation and solve it to find the maximum number of people that can attend the event within the given budget.

Conclusion

In conclusion, the mathematical problem of determining the maximum number of friends that can visit the amusement park within a given budget is a classic example of a linear inequality. By solving the inequality, we can determine the maximum number of friends that can visit the park within the given budget. We hope that this Q&A article has provided you with a better understanding of this mathematical problem and its real-world applications.