Will's Company Offers A Reimbursement Package Of $\$0.59$ Per Mile Plus $\$275$ A Year For Maintenance. If $x$ Represents The Number Of Miles, Which Equation Below Models $C$, The Total Amount Of Reimbursement The

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Will's company offers a reimbursement package that includes a certain amount of money per mile driven, plus a fixed amount for maintenance. In this scenario, we are given that the reimbursement package is $0.59\$0.59 per mile plus $275\$275 a year for maintenance. We need to determine the equation that models the total amount of reimbursement, denoted as CC, in terms of the number of miles driven, represented by xx.

The Equation

To model the total amount of reimbursement, we need to consider both the reimbursement per mile and the fixed maintenance amount. The reimbursement per mile is a linear function of the number of miles driven, while the fixed maintenance amount is a constant. Therefore, the equation that models the total amount of reimbursement can be represented as:

C = 0.59x + 275

In this equation, CC represents the total amount of reimbursement, xx represents the number of miles driven, and 0.590.59 is the reimbursement per mile. The fixed maintenance amount of $275\$275 is added to the reimbursement per mile to obtain the total amount of reimbursement.

Interpreting the Equation

Let's break down the equation and understand what each component represents.

  • C: The total amount of reimbursement, which is the sum of the reimbursement per mile and the fixed maintenance amount.
  • 0.59x: The reimbursement per mile, which is a linear function of the number of miles driven. For every mile driven, the company reimburses $0.59\$0.59.
  • 275: The fixed maintenance amount, which is a constant added to the reimbursement per mile to obtain the total amount of reimbursement.

Example

Suppose Will drives 500 miles in a year. To calculate the total amount of reimbursement, we can plug in the value of xx into the equation:

C = 0.59(500) + 275

C = 295 + 275

C = 570

Therefore, the total amount of reimbursement for driving 500 miles in a year is $570\$570.

Conclusion

In conclusion, the equation that models the total amount of reimbursement is C = 0.59x + 275. This equation represents the reimbursement per mile as a linear function of the number of miles driven, plus a fixed maintenance amount. By plugging in the value of xx, we can calculate the total amount of reimbursement for a given number of miles driven.

Will's company offers a reimbursement package that includes a certain amount of money per mile driven, plus a fixed amount for maintenance. In this scenario, we are given that the reimbursement package is $0.59\$0.59 per mile plus $275\$275 a year for maintenance. We need to determine the equation that models the total amount of reimbursement, denoted as CC, in terms of the number of miles driven, represented by xx.

The Equation

To model the total amount of reimbursement, we need to consider both the reimbursement per mile and the fixed maintenance amount. The reimbursement per mile is a linear function of the number of miles driven, while the fixed maintenance amount is a constant. Therefore, the equation that models the total amount of reimbursement can be represented as:

C = 0.59x + 275

In this equation, CC represents the total amount of reimbursement, xx represents the number of miles driven, and 0.590.59 is the reimbursement per mile. The fixed maintenance amount of $275\$275 is added to the reimbursement per mile to obtain the total amount of reimbursement.

Interpreting the Equation

Let's break down the equation and understand what each component represents.

  • C: The total amount of reimbursement, which is the sum of the reimbursement per mile and the fixed maintenance amount.
  • 0.59x: The reimbursement per mile, which is a linear function of the number of miles driven. For every mile driven, the company reimburses $0.59\$0.59.
  • 275: The fixed maintenance amount, which is a constant added to the reimbursement per mile to obtain the total amount of reimbursement.

Example

Suppose Will drives 500 miles in a year. To calculate the total amount of reimbursement, we can plug in the value of xx into the equation:

C = 0.59(500) + 275

C = 295 + 275

C = 570

Therefore, the total amount of reimbursement for driving 500 miles in a year is $570\$570.

Conclusion

In conclusion, the equation that models the total amount of reimbursement is C = 0.59x + 275. This equation represents the reimbursement per mile as a linear function of the number of miles driven, plus a fixed maintenance amount. By plugging in the value of xx, we can calculate the total amount of reimbursement for a given number of miles driven.

Graphing the Equation

To visualize the relationship between the number of miles driven and the total amount of reimbursement, we can graph the equation C = 0.59x + 275.

Graph

The graph of the equation C = 0.59x + 275 is a straight line with a slope of 0.590.59 and a y-intercept of 275275. The x-axis represents the number of miles driven, and the y-axis represents the total amount of reimbursement.

Interpreting the Graph

Let's analyze the graph and understand what it represents.

  • Slope: The slope of the graph represents the reimbursement per mile, which is 0.590.59. For every mile driven, the company reimburses $0.59\$0.59.
  • Y-intercept: The y-intercept of the graph represents the fixed maintenance amount, which is 275275. This is the amount that the company reimburses regardless of the number of miles driven.
  • Linearity: The graph is a straight line, indicating that the relationship between the number of miles driven and the total amount of reimbursement is linear.

Conclusion

In conclusion, the graph of the equation C = 0.59x + 275 represents the relationship between the number of miles driven and the total amount of reimbursement. The graph is a straight line with a slope of 0.590.59 and a y-intercept of 275275, indicating that the relationship is linear.

Real-World Applications

The equation C = 0.59x + 275 has several real-world applications.

  • Business: The equation can be used by companies to calculate the total amount of reimbursement for employees who drive company vehicles.
  • Finance: The equation can be used by financial institutions to calculate the total amount of reimbursement for individuals who drive company vehicles.
  • Taxation: The equation can be used by tax authorities to calculate the total amount of reimbursement for individuals who drive company vehicles.

Conclusion

In our previous article, we discussed the reimbursement package offered by Will's company, which includes a certain amount of money per mile driven, plus a fixed amount for maintenance. We also derived the equation C = 0.59x + 275 to model the total amount of reimbursement in terms of the number of miles driven, represented by xx. In this article, we will answer some frequently asked questions related to the reimbursement package and the equation.

Q: What is the reimbursement per mile?

A: The reimbursement per mile is $0.59\$0.59. This means that for every mile driven, the company reimburses $0.59\$0.59.

Q: What is the fixed maintenance amount?

A: The fixed maintenance amount is $275\$275. This is the amount that the company reimburses regardless of the number of miles driven.

Q: How do I calculate the total amount of reimbursement?

A: To calculate the total amount of reimbursement, you can use the equation C = 0.59x + 275, where CC represents the total amount of reimbursement, xx represents the number of miles driven, and 0.590.59 is the reimbursement per mile.

Q: What if I drive more than 500 miles in a year?

A: If you drive more than 500 miles in a year, you can simply plug in the value of xx into the equation C = 0.59x + 275 to calculate the total amount of reimbursement.

Q: Can I use the equation to calculate the reimbursement for a specific number of miles driven?

A: Yes, you can use the equation C = 0.59x + 275 to calculate the reimbursement for a specific number of miles driven. For example, if you drive 750 miles in a year, you can plug in the value of xx into the equation to calculate the total amount of reimbursement.

Q: What if I have a different reimbursement rate per mile?

A: If you have a different reimbursement rate per mile, you can simply replace the value of 0.590.59 in the equation C = 0.59x + 275 with your own reimbursement rate.

Q: Can I use the equation to calculate the reimbursement for a specific number of years?

A: Yes, you can use the equation C = 0.59x + 275 to calculate the reimbursement for a specific number of years. For example, if you drive 500 miles per year for 5 years, you can multiply the value of xx by 5 and plug it into the equation to calculate the total amount of reimbursement.

Q: What if I have a different fixed maintenance amount?

A: If you have a different fixed maintenance amount, you can simply replace the value of 275275 in the equation C = 0.59x + 275 with your own fixed maintenance amount.

Conclusion

In conclusion, the equation C = 0.59x + 275 is a useful tool for calculating the total amount of reimbursement for individuals who drive company vehicles. By understanding the reimbursement package and the equation, you can calculate the total amount of reimbursement for a given number of miles driven. We hope this Q&A article has helped to clarify any questions you may have had about the reimbursement package and the equation.

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Related Articles

  • Understanding the Reimbursement Package: This article discusses the reimbursement package offered by Will's company and derives the equation C = 0.59x + 275 to model the total amount of reimbursement.
  • Graphing the Equation: This article discusses how to graph the equation C = 0.59x + 275 and interpret the results.
  • Real-World Applications: This article discusses the real-world applications of the equation C = 0.59x + 275, including business, finance, and taxation.