Chau Took A Taxi To The Train Station. He Paid The Driver A Fee Of $$ 146$ And Gave Her An Additional $15%$ Tip. (a) Let $x$ Be The Amount Chau Gave As A Tip (in Dollars). Using The Values Below, Create A
Introduction
In this discussion, we will delve into a mathematical problem involving a taxi fare and a tip. Chau took a taxi to the train station and paid the driver a fee of $146, along with an additional 15% tip. We will use the values provided to create an equation and solve for the amount Chau gave as a tip.
Given Values
- The total amount paid by Chau is $146.
- The tip given by Chau is 15% of the total amount paid.
Creating an Equation
Let's denote the amount Chau gave as a tip as x. We can create an equation using the given values:
Total amount paid = Tip + Fare 146 = x + 146
Simplifying the Equation
To solve for x, we need to isolate the variable. We can do this by subtracting 146 from both sides of the equation:
x = 146 - 146 x = 0
Interpretation of the Result
At first glance, the result may seem counterintuitive. However, it's essential to understand that the equation we created is based on the given values. The tip given by Chau is 15% of the total amount paid, which is $146. To find the amount of the tip, we need to calculate 15% of $146.
Calculating the Tip
To calculate the tip, we can multiply the total amount paid by 0.15 (which is equivalent to 15%):
Tip = 0.15 x 146 Tip = 21.90
Conclusion
In conclusion, the amount Chau gave as a tip is $21.90, not $0. This result is based on the correct calculation of 15% of the total amount paid. The initial result of $0 was due to the incorrect simplification of the equation.
Discussion
This problem highlights the importance of careful calculation and attention to detail when working with mathematical equations. It also demonstrates the need to interpret the results in the context of the problem.
Mathematical Concepts
This problem involves the following mathematical concepts:
- Algebraic equations
- Percentages
- Calculations
Real-World Applications
This problem has real-world applications in various fields, such as finance, economics, and business. Understanding how to calculate tips and percentages is essential in these fields.
Tips for Solving Similar Problems
When solving similar problems, remember to:
- Carefully read and understand the problem statement
- Identify the given values and the unknown variable
- Create an equation based on the given values
- Simplify the equation correctly
- Interpret the results in the context of the problem
Q&A: Understanding Tips and Percentages =============================================
Introduction
In our previous discussion, we explored a mathematical problem involving a taxi fare and a tip. We created an equation and solved for the amount Chau gave as a tip. In this Q&A article, we will address some common questions related to tips and percentages.
Q: What is a tip, and why is it important?
A: A tip is a gratuity or a small amount of money given to someone, usually in appreciation of their service. In the context of the problem, the tip is 15% of the total amount paid. Understanding tips and percentages is essential in various fields, such as finance, economics, and business.
Q: How do I calculate a tip?
A: To calculate a tip, you need to multiply the total amount by the percentage of the tip. For example, if the total amount is $146 and the tip is 15%, you can calculate the tip as follows:
Tip = 0.15 x 146 Tip = 21.90
Q: What is the difference between a tip and a gratuity?
A: A tip and a gratuity are often used interchangeably, but there is a subtle difference. A tip is a voluntary payment made to someone in appreciation of their service, while a gratuity is a mandatory payment made in certain situations, such as in restaurants or bars.
Q: How do I calculate a percentage?
A: To calculate a percentage, you need to divide the part by the whole and multiply by 100. For example, if you want to calculate 15% of $146, you can do the following:
15% = (15/100) x 146 15% = 0.15 x 146 15% = 21.90
Q: What are some common percentage calculations?
A: Some common percentage calculations include:
- 10% of a number: 0.10 x number
- 20% of a number: 0.20 x number
- 5% of a number: 0.05 x number
Q: How do I apply percentage calculations in real-life situations?
A: Percentage calculations have numerous applications in real-life situations, such as:
- Calculating sales tax or tips in restaurants
- Determining interest rates on loans or investments
- Understanding profit margins in business
Q: What are some common mistakes to avoid when calculating percentages?
A: Some common mistakes to avoid when calculating percentages include:
- Forgetting to multiply by 100 when converting a decimal to a percentage
- Not using the correct percentage sign (%)
- Not rounding correctly when dealing with decimal numbers
Conclusion
In conclusion, understanding tips and percentages is essential in various fields, such as finance, economics, and business. By mastering percentage calculations, you can apply them in real-life situations and make informed decisions. Remember to avoid common mistakes and always double-check your calculations.
Tips for Mastering Percentage Calculations
- Practice, practice, practice: The more you practice percentage calculations, the more comfortable you will become with them.
- Use online resources: There are numerous online resources available that can help you master percentage calculations, such as calculators and tutorials.
- Apply percentage calculations in real-life situations: The best way to learn percentage calculations is by applying them in real-life situations.