Calculating the Purchase Fee

Oct 13, 2025 by pinkandtrash.com 92 views

Introduction

Mathematics is an essential part of our daily lives, and it's not just limited to solving equations and formulas. In real-world scenarios, math is used to make informed decisions, calculate costs, and make predictions. In this article, we will explore a real-world math problem and learn how to solve it step by step.

The Problem

Sam has $20 and wants to buy the new Grand Theft Auto game for his Nintendo Switch, which costs $52.24 plus a 5% purchase fee. He decides to mow lawns in the neighborhood for $7 per hour to earn enough money to buy the game. We need to write an equation that represents the situation and then solve it to find out how many hours Sam needs to work to buy the game.

Writing the Equation

Let's break down the problem and write an equation that represents the situation. We know that Sam needs to earn enough money to buy the game, which costs $52.24 plus a 5% purchase fee. The purchase fee is 5% of the cost of the game, which is $52.24. To calculate the purchase fee, we need to multiply the cost of the game by 0.05.

Calculating the Purchase Fee

The purchase fee is calculated as follows:

Purchase fee = 0.05 x $52.24 Purchase fee = $2.61

The Total Cost

The total cost of the game is the cost of the game plus the purchase fee:

Total cost = $52.24 + $2.61 Total cost = $54.85

The Equation

Now that we have the total cost, we can write an equation that represents the situation. Let's say x is the number of hours Sam needs to work to earn enough money to buy the game. The equation is:

7x = 54.85

Solving the Equation

To solve the equation, we need to isolate x. We can do this by dividing both sides of the equation by 7:

x = 54.85 ÷ 7 x = 7.83

Conclusion

Sam needs to work for approximately 7.83 hours to earn enough money to buy the new Grand Theft Auto game for his Nintendo Switch. This is a real-world math problem that requires us to use our knowledge of algebra and percentages to solve. By breaking down the problem and writing an equation that represents the situation, we can find the solution and make informed decisions.

Real-World Applications

This problem has real-world applications in many areas, such as:

Finance: When buying a product or service, we need to consider the cost and any additional fees.
Business: When calculating the cost of a product or service, we need to consider the cost of production, marketing, and distribution.
Personal Finance: When budgeting and saving money, we need to consider our income and expenses.

Tips and Tricks

When solving real-world math problems, here are some tips and tricks to keep in mind:

Break down the problem: Break down the problem into smaller, manageable parts.
Write an equation: Write an equation that represents the situation.
Use algebra: Use algebra to solve the equation.
Consider real-world applications: Consider how the problem applies to real-world scenarios.

Conclusion

Introduction

In our previous article, we explored a real-world math problem and learned how to solve it step by step. In this article, we will answer some frequently asked questions about solving real-world math problems.

Q: What is the most important thing to consider when solving a real-world math problem?

A: The most important thing to consider when solving a real-world math problem is to break down the problem into smaller, manageable parts. This will help you to identify the key elements of the problem and make it easier to solve.

Q: How do I know if I have the right solution to a real-world math problem?

A: To know if you have the right solution to a real-world math problem, you need to check your work and make sure that your solution makes sense in the context of the problem. You should also consider the real-world applications of the problem and make sure that your solution is practical and feasible.

Q: What are some common mistakes to avoid when solving real-world math problems?

A: Some common mistakes to avoid when solving real-world math problems include:

Not breaking down the problem: Failing to break down the problem into smaller, manageable parts can make it difficult to solve.
Not considering real-world applications: Failing to consider the real-world applications of the problem can lead to impractical or unrealistic solutions.
Not checking your work: Failing to check your work can lead to errors and incorrect solutions.

Q: How can I practice solving real-world math problems?

A: There are many ways to practice solving real-world math problems, including:

Using online resources: There are many online resources available that provide real-world math problems and solutions.
Working with a tutor: Working with a tutor can provide you with personalized guidance and support as you practice solving real-world math problems.
Solving problems in your daily life: Solving problems in your daily life, such as budgeting and saving money, can help you to develop your problem-solving skills and apply them to real-world scenarios.

Q: What are some real-world math problems that I can practice solving?

A: Some real-world math problems that you can practice solving include:

Budgeting and saving money: Calculating your income and expenses, and creating a budget to save money.
Investing: Calculating the return on investment (ROI) of a stock or other investment.
Travel: Calculating the cost of a trip, including transportation, accommodation, and food.

Q: How can I apply my knowledge of real-world math problems to my career?

A: Your knowledge of real-world math problems can be applied to many careers, including:

Finance: Calculating the cost of a product or service, and creating a budget to save money.
Business: Calculating the ROI of a business investment, and creating a budget to save money.
Science: Calculating the cost of a scientific experiment, and creating a budget to save money.

Conclusion

In conclusion, solving real-world math problems requires a combination of mathematical knowledge and practical problem-solving skills. By breaking down the problem, considering real-world applications, and checking your work, you can develop your problem-solving skills and apply them to real-world scenarios. With practice and experience, you can become proficient in solving real-world math problems and apply your knowledge to many areas of your life.

Additional Resources

For more information on solving real-world math problems, check out the following resources:

Online resources: Websites such as Khan Academy, Mathway, and Wolfram Alpha provide real-world math problems and solutions.
Books: Books such as "Real-World Math" by David M. Bressoud and "Mathematics for the Nonmathematician" by Morris Kline provide a comprehensive introduction to real-world math problems.
Tutors: Working with a tutor can provide you with personalized guidance and support as you practice solving real-world math problems.