The Weekly Allowance and Extra Earnings

Oct 13, 2025 by miodeya.com 50 views

Introduction

Jade and Chet are two individuals who receive a weekly allowance, in addition to earning extra money by walking the dog. The amount they earn from walking the dog is denoted by $x$ dollars. In this article, we will explore their combined earnings for a certain week and how they plan to save a portion of it to purchase a new app for their smart tablet.

The Weekly Allowance and Extra Earnings

Let's assume that Jade and Chet receive a weekly allowance of $a$ dollars each. They also earn an extra $x$ dollars each time they walk the dog. If they walk the dog $n$ times in a week, their total earnings from walking the dog would be $nx$ dollars.

Their combined earnings for a certain week can be represented as:

\text{Combined Earnings} = a + a + nx = 2a + nx

Saving a Portion of Their Earnings

Jade and Chet plan to save $40\%$ of their combined earnings to purchase a new app for their smart tablet. This means that they will save $0.4(2a + nx)$ dollars and spend the remaining amount on the app.

Calculating the Amount Saved

To calculate the amount saved, we need to multiply their combined earnings by $0.4$ :

\text{Amount Saved} = 0.4(2a + nx) = 0.8a + 0.4nx

Calculating the Amount Spent

The amount spent on the app is the difference between their combined earnings and the amount saved:

\text{Amount Spent} = (2a + nx) - (0.8a + 0.4nx) = 1.2a + 0.6nx

Simplifying the Expressions

We can simplify the expressions for the amount saved and the amount spent by factoring out the common terms:

\text{Amount Saved} = 0.8a + 0.4nx = 0.8a + 0.4n(x)

\text{Amount Spent} = 1.2a + 0.6nx = 1.2a + 0.6n(x)

Conclusion

In this article, we explored the combined earnings of Jade and Chet for a certain week and how they plan to save a portion of it to purchase a new app for their smart tablet. We calculated the amount saved and the amount spent on the app using their combined earnings and the percentage they plan to save.

Real-World Applications

This problem can be applied to real-world scenarios where individuals receive a weekly allowance and earn extra money by performing tasks or services. For example, a teenager who receives a weekly allowance and earns extra money by mowing lawns or walking dogs can use this problem to calculate their combined earnings and plan their savings.

Future Directions

In the future, we can explore more complex scenarios where individuals receive a variable weekly allowance and earn extra money by performing tasks or services. We can also consider scenarios where individuals have different savings goals and need to calculate their savings based on their individual goals.

References

[1] "Mathematics for Dummies" by Mark Ryan
[2] "Algebra and Trigonometry" by James Stewart

Appendix

The following is a list of formulas and equations used in this article:

Combined Earnings: $2a + nx$
Amount Saved: $0.8a + 0.4nx$
Amount Spent: $(2a + nx) - (0.8a + 0.4nx)$

Introduction

In our previous article, we explored the combined earnings of Jade and Chet for a certain week and how they plan to save a portion of it to purchase a new app for their smart tablet. In this article, we will answer some frequently asked questions related to their allowance and earnings.

Q: What is the formula for calculating the combined earnings of Jade and Chet?

A: The formula for calculating the combined earnings of Jade and Chet is:

\text{Combined Earnings} = 2a + nx

where $a$ is the weekly allowance and $x$ is the amount earned from walking the dog.

Q: How do Jade and Chet plan to save their earnings?

A: Jade and Chet plan to save $40\%$ of their combined earnings to purchase a new app for their smart tablet.

Q: What is the formula for calculating the amount saved by Jade and Chet?

A: The formula for calculating the amount saved by Jade and Chet is:

\text{Amount Saved} = 0.8a + 0.4nx

Q: What is the formula for calculating the amount spent by Jade and Chet?

A: The formula for calculating the amount spent by Jade and Chet is:

\text{Amount Spent} = 1.2a + 0.6nx

Q: Can you explain the concept of percentage in the context of Jade and Chet's earnings?

A: Yes, in the context of Jade and Chet's earnings, the percentage refers to the proportion of their combined earnings that they plan to save. In this case, they plan to save $40\%$ of their combined earnings, which means they will save $0.4(2a + nx)$ dollars and spend the remaining amount on the app.

Q: How can I apply this concept to my own life?

A: This concept can be applied to your own life by considering your own earnings and savings goals. For example, if you receive a weekly allowance and earn extra money by performing tasks or services, you can use the formulas provided to calculate your combined earnings and plan your savings.

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

A: Some real-world applications of this concept include:

Calculating the earnings of a teenager who receives a weekly allowance and earns extra money by mowing lawns or walking dogs
Planning the savings of a family who receives a weekly allowance and earns extra money by performing tasks or services
Calculating the earnings of a business that receives a weekly allowance and earns extra money by providing services

Q: Can you provide some examples of how to use the formulas in real-world scenarios?

A: Yes, here are some examples of how to use the formulas in real-world scenarios:

Example 1: A teenager receives a weekly allowance of $20 and earns an extra $10 for walking the dog. If they walk the dog 5 times in a week, their combined earnings would be:

\text{Combined Earnings} = 2(20) + 5(10) = 40 + 50 = 90

They plan to save $40\%$ of their combined earnings, which would be:

\text{Amount Saved} = 0.8(90) = 72

They would spend the remaining amount on the app.

Example 2: A family receives a weekly allowance of $50 and earns an extra $20 for performing tasks or services. If they perform tasks or services 3 times in a week, their combined earnings would be:

\text{Combined Earnings} = 2(50) + 3(20) = 100 + 60 = 160

They plan to save $40\%$ of their combined earnings, which would be:

\text{Amount Saved} = 0.8(160) = 128

They would spend the remaining amount on the app.

Conclusion

In this article, we answered some frequently asked questions related to the allowance and earnings of Jade and Chet. We provided formulas and examples to help you understand the concept and apply it to your own life.