Danae Is Choosing Between Two Jobs. One Job Pays An Annual Bonus Of $\$1,500$ Plus $\$120$ Per Day Worked. The Second Job Pays An Annual Bonus Of $\$2,500$ Plus $\$110$ Per Day Worked. Which Equation Can Be Solved To

Introduction

When it comes to making a decision about a job, there are many factors to consider. Salary, benefits, work-life balance, and opportunities for growth are just a few of the things that can influence our choice. In this article, we will explore a scenario where Danae is faced with a difficult decision between two job offers. We will examine the equations that can be used to solve this problem and provide a step-by-step guide on how to make a decision.

The Problem

Danae is considering two job offers. The first job pays an annual bonus of $\$1,500$ plus $\$120$ per day worked. The second job pays an annual bonus of $\$2,500$ plus $\$110$ per day worked. Danae wants to know which job will pay her more in a year, assuming she works the same number of days in both jobs.

Let's Break Down the Problem

To solve this problem, we need to create an equation that represents the total amount of money Danae will earn in each job. Let's start by defining some variables:

• $x$ = number of days worked in a year
• $y$ = total amount of money earned in a year

For the first job, the total amount of money earned in a year can be represented by the equation:

$$y = 1500 + 120x$$

This equation states that the total amount of money earned in a year is equal to the annual bonus of $\$1,500$ plus the daily bonus of $\$120$ multiplied by the number of days worked.

For the second job, the total amount of money earned in a year can be represented by the equation:

$$y = 2500 + 110x$$

This equation states that the total amount of money earned in a year is equal to the annual bonus of $\$2,500$ plus the daily bonus of $\$110$ multiplied by the number of days worked.

Which Equation Can Be Solved to Determine Which Job Pays More?

To determine which job pays more, we need to compare the two equations. We can do this by setting the two equations equal to each other and solving for $x$.

$$1500 + 120x = 2500 + 110x$$

Subtracting $110x$ from both sides gives us:

$$1500 + 10x = 2500$$

Subtracting $1500$ from both sides gives us:

$$10x = 1000$$

Dividing both sides by $10$ gives us:

$$x = 100$$

This means that if Danae works $100$ days in a year, the first job will pay her more. However, if she works more than $100$ days, the second job will pay her more.

Conclusion

In conclusion, the equation that can be solved to determine which job pays more is:

$$1500 + 120x = 2500 + 110x$$

By setting the two equations equal to each other and solving for $x$, we can determine the number of days that Danae needs to work in order to make the first job more lucrative than the second job.

Real-World Applications

This problem has many real-world applications. For example, when considering a job offer, it's essential to factor in the total compensation package, including bonuses, benefits, and other perks. By using equations like the one above, individuals can make informed decisions about which job is best for them.

Tips for Solving Similar Problems

When solving similar problems, remember to:

• Define variables clearly and consistently
• Create equations that represent the problem
• Set the equations equal to each other and solve for the variable
• Consider the real-world implications of the solution

By following these tips, you can become proficient in solving problems like this and make informed decisions about your career.

Final Thoughts

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Q&A: Frequently Asked Questions About Danae's Job Dilemma

Q: What is the main difference between the two job offers?

A: The main difference between the two job offers is the annual bonus and the daily bonus. The first job pays an annual bonus of $\$1,500$ plus $\$120$ per day worked, while the second job pays an annual bonus of $\$2,500$ plus $\$110$ per day worked.

Q: How can I determine which job pays more?

A: To determine which job pays more, you can set the two equations equal to each other and solve for $x$. This will give you the number of days that you need to work in order to make the first job more lucrative than the second job.

Q: What is the equation that can be used to solve this problem?

A: The equation that can be used to solve this problem is:

$$1500 + 120x = 2500 + 110x$$

Q: How do I solve this equation?

A: To solve this equation, you can follow these steps:

1. Subtract $110x$ from both sides of the equation.
2. Subtract $1500$ from both sides of the equation.
3. Divide both sides of the equation by $10$.

Q: What is the solution to this equation?

A: The solution to this equation is $x = 100$. This means that if you work $100$ days in a year, the first job will pay you more.

Q: What if I work more than 100 days in a year?

A: If you work more than $100$ days in a year, the second job will pay you more.

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

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

• Considering a job offer and factoring in the total compensation package
• Making informed decisions about career choices
• Using algebraic equations to solve problems in business and finance

Q: What are some tips for solving similar problems?

A: Some tips for solving similar problems include:

• Defining variables clearly and consistently
• Creating equations that represent the problem
• Setting the equations equal to each other and solving for the variable
• Considering the real-world implications of the solution

Q: Can I use this equation to solve other problems?

A: Yes, you can use this equation to solve other problems that involve comparing two different options. For example, you can use this equation to compare two different investment options or two different loan offers.

Q: Is there a way to simplify this equation?

A: Yes, you can simplify this equation by combining like terms. For example, you can rewrite the equation as:

$$10x = 1000$$

This makes it easier to solve the equation and find the solution.

Q: Can I use this equation to solve problems with more than two variables?

A: Yes, you can use this equation to solve problems with more than two variables. However, you will need to create a system of equations and use algebraic techniques to solve the problem.

Q: Is there a way to visualize this problem?

A: Yes, you can visualize this problem by creating a graph or a chart. For example, you can create a graph of the two equations and see where they intersect. This can help you understand the problem and find the solution.