Last Week, Lindsay Earned \[$\$10\$\] Per Hour Plus A \[$\$60\$\] Bonus For Good Job Performance. She Spends \[$\frac{1}{15}\$\] Of Her Paycheck On Dinner With Friends. If She Had Not Earned The Bonus, The Amount She Spent On

Feb 26, 2025 by ADMIN 226 views

The Art of Calculating Earnings and Expenses: A Mathematical Exploration

In the world of mathematics, problems often arise from real-life scenarios, requiring us to apply mathematical concepts to solve them. In this article, we will delve into a problem involving earnings and expenses, using mathematical techniques to find the solution. Our protagonist, Lindsay, has earned a certain amount of money per hour, plus a bonus for good job performance. We will explore how she spends her paycheck and calculate the amount she would have spent if she hadn't earned the bonus.

Lindsay earns $10 per hour, plus a $60 bonus for good job performance. This means that her total earnings for the week are the sum of her hourly wage and the bonus. Let's denote her total earnings as E. We can express this as:

E = $10 (hourly wage) + $60 (bonus)

E = $70

So, Lindsay's total earnings for the week are $70.

Lindsay spends \frac{1}{15} of her paycheck on dinner with friends. To find the amount she spends on dinner, we need to multiply her total earnings by the fraction representing the amount spent on dinner. Let's denote the amount spent on dinner as D. We can express this as:

D = E × \frac{1}{15}

D = $70 × \frac{1}{15}

D = $4.67

So, Lindsay spends $4.67 on dinner with friends.

Now, let's consider a scenario where Lindsay hadn't earned the bonus. In this case, her total earnings would be the hourly wage only, which is $10 per hour. We can express this as:

E' = $10 (hourly wage)

E' = $10 × x (number of hours worked)

where x is the number of hours Lindsay worked.

To find the amount she would have spent on dinner if she hadn't earned the bonus, we need to multiply her new total earnings by the fraction representing the amount spent on dinner. Let's denote the new amount spent on dinner as D'. We can express this as:

D' = E' × \frac{1}{15}

D' = $10 × x × \frac{1}{15}

D' = $0.67 × x

So, the amount Lindsay would have spent on dinner if she hadn't earned the bonus is $0.67 times the number of hours she worked.

In this article, we explored a problem involving earnings and expenses, using mathematical techniques to find the solution. We calculated Lindsay's total earnings, the amount she spent on dinner, and the amount she would have spent on dinner if she hadn't earned the bonus. By applying mathematical concepts, we were able to find the answers to these questions and gain a deeper understanding of the problem.

Lindsay earns $10 per hour, plus a $60 bonus for good job performance.
She spends \frac{1}{15} of her paycheck on dinner with friends.
If she hadn't earned the bonus, the amount she would have spent on dinner is $0.67 times the number of hours she worked.

This problem can be extended to explore other mathematical concepts, such as:

Calculating the total amount spent on dinner over a period of time.
Finding the average amount spent on dinner per hour.
Exploring the relationship between Lindsay's earnings and her spending habits.

By applying mathematical techniques to real-life scenarios, we can gain a deeper understanding of the world around us and develop problem-solving skills that can be applied to a wide range of situations.
Frequently Asked Questions: Earnings and Expenses

In our previous article, we explored a problem involving earnings and expenses, using mathematical techniques to find the solution. We calculated Lindsay's total earnings, the amount she spent on dinner, and the amount she would have spent on dinner if she hadn't earned the bonus. In this article, we will answer some frequently asked questions related to the problem.

Q: What is the total amount Lindsay earns per week?

A: Lindsay earns $10 per hour, plus a $60 bonus for good job performance. Her total earnings for the week are $70.

Q: How much does Lindsay spend on dinner with friends?

A: Lindsay spends \frac{1}{15} of her paycheck on dinner with friends. This is equivalent to $4.67.

Q: What if Lindsay hadn't earned the bonus? How much would she have spent on dinner?

A: If Lindsay hadn't earned the bonus, her total earnings would be $10 per hour. The amount she would have spent on dinner is $0.67 times the number of hours she worked.

Q: How can I calculate the total amount spent on dinner over a period of time?

A: To calculate the total amount spent on dinner over a period of time, you can multiply the amount spent on dinner per hour by the number of hours worked. For example, if Lindsay works 40 hours per week and spends $4.67 on dinner per hour, the total amount spent on dinner per week is $4.67 × 40 = $186.80.

Q: What is the average amount spent on dinner per hour?

A: To find the average amount spent on dinner per hour, you can divide the total amount spent on dinner by the number of hours worked. For example, if Lindsay works 40 hours per week and spends $186.80 on dinner, the average amount spent on dinner per hour is $186.80 ÷ 40 = $4.67.

Q: How can I explore the relationship between Lindsay's earnings and her spending habits?

A: You can explore the relationship between Lindsay's earnings and her spending habits by analyzing how changes in her earnings affect her spending habits. For example, if Lindsay's earnings increase by $10, you can calculate how much her spending habits will change.

In this article, we answered some frequently asked questions related to the problem of earnings and expenses. We provided step-by-step solutions to each question, using mathematical techniques to find the answers. By applying mathematical concepts to real-life scenarios, we can gain a deeper understanding of the world around us and develop problem-solving skills that can be applied to a wide range of situations.

Lindsay earns $10 per hour, plus a $60 bonus for good job performance.
She spends \frac{1}{15} of her paycheck on dinner with friends.
If she hadn't earned the bonus, the amount she would have spent on dinner is $0.67 times the number of hours she worked.

This problem can be extended to explore other mathematical concepts, such as:

Calculating the total amount spent on dinner over a period of time.
Finding the average amount spent on dinner per hour.
Exploring the relationship between Lindsay's earnings and her spending habits.