Tim's Company Offers A Reimbursement Package Of $ 0.65 \$0.65 $0.65 Per Mile Plus $ 145 \$145 $145 A Year For Maintenance. If X X X Represents The Number Of Miles, Which Equation Below Models C C C , The Total Amount Of Reimbursement The

Tim's company offers a reimbursement package of $$0.65$ This reimbursement package is designed to compensate employees for their expenses related to business travel and vehicle maintenance. The reimbursement amount is calculated based on the number of miles driven and the annual maintenance cost.

Modeling the Reimbursement Amount

Let's assume that $x$ represents the number of miles driven. The reimbursement amount for each mile is $\$0.65$. Therefore, the total reimbursement amount for $x$ miles can be calculated as $0.65x$. Additionally, the company also provides a fixed reimbursement of $\$145$ per year for maintenance. To model the total reimbursement amount, we need to add the reimbursement for miles driven and the annual maintenance cost.

Equation Modeling the Reimbursement Amount

The equation that models the total reimbursement amount $C$ is given by:

$$C = 0.65x + 145$$

This equation represents the reimbursement package offered by Tim's company. The variable $x$ represents the number of miles driven, and the constant $0.65$ represents the reimbursement amount per mile. The constant $145$ represents the annual maintenance cost.

Interpreting the Equation

The equation $C = 0.65x + 145$ can be interpreted as follows:

• The term $0.65x$ represents the reimbursement amount for the number of miles driven. For every mile driven, the employee receives $\$0.65$ as reimbursement.
• The term $145$ represents the annual maintenance cost. This is a fixed cost that is reimbursed to the employee regardless of the number of miles driven.

Example

Suppose Tim drives $200$ miles in a year. The total reimbursement amount can be calculated using the equation:

$$C = 0.65(200) + 145$$

$$C = 130 + 145$$

$$C = 275$$

Therefore, the total reimbursement amount for Tim is $\$275$.

Conclusion

In conclusion, the equation $C = 0.65x + 145$ models the reimbursement package offered by Tim's company. The equation represents the reimbursement amount for the number of miles driven and the annual maintenance cost. By using this equation, we can calculate the total reimbursement amount for any given number of miles driven.

Understanding the Components of the Equation

The equation $C = 0.65x + 145$ consists of two components:

• The term $0.65x$ represents the reimbursement amount for the number of miles driven.
• The term $145$ represents the annual maintenance cost.

Calculating the Reimbursement Amount

To calculate the reimbursement amount, we need to multiply the number of miles driven by the reimbursement amount per mile ($0.65$) and add the annual maintenance cost ($145$).

Example Calculations

Suppose Tim drives $x$ miles in a year. The total reimbursement amount can be calculated using the equation:

$$C = 0.65x + 145$$

For example, if Tim drives $200$ miles, the total reimbursement amount is:

$$C = 0.65(200) + 145$$

$$C = 130 + 145$$

$$C = 275$$

Therefore, the total reimbursement amount for Tim is $\$275$.

Graphing the Equation

The equation $C = 0.65x + 145$ can be graphed on a coordinate plane. The graph will be a straight line with a slope of $0.65$ and a y-intercept of $145$.

Interpreting the Graph

The graph of the equation $C = 0.65x + 145$ can be interpreted as follows:

• The slope of the line represents the reimbursement amount per mile ($0.65$).
• The y-intercept of the line represents the annual maintenance cost ($145$).

Conclusion

In conclusion, the equation $C = 0.65x + 145$ models the reimbursement package offered by Tim's company. The equation represents the reimbursement amount for the number of miles driven and the annual maintenance cost. By using this equation, we can calculate the total reimbursement amount for any given number of miles driven.

Understanding the Relationship Between the Equation and the Graph

The equation $C = 0.65x + 145$ and the graph of the equation are related in the following way:

• The equation represents the reimbursement amount for the number of miles driven and the annual maintenance cost.
• The graph of the equation represents the relationship between the reimbursement amount and the number of miles driven.

Conclusion

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Q: What is the reimbursement package offered by Tim's company?

A: The reimbursement package offered by Tim's company is $\$0.65$ per mile plus $\$145$ a year for maintenance.

Q: How is the reimbursement amount calculated?

A: The reimbursement amount is calculated by multiplying the number of miles driven by the reimbursement amount per mile ($0.65$) and adding the annual maintenance cost ($145$).

Q: What is the equation that models the reimbursement amount?

A: The equation that models the reimbursement amount is $C = 0.65x + 145$, where $C$ is the total reimbursement amount and $x$ is the number of miles driven.

Q: How can I use the equation to calculate the reimbursement amount?

A: To use the equation to calculate the reimbursement amount, simply plug in the number of miles driven ($x$) and solve for $C$. For example, if Tim drives $200$ miles, the total reimbursement amount is:

$$C = 0.65(200) + 145$$

$$C = 130 + 145$$

$$C = 275$$

Q: What is the slope of the line that represents the reimbursement amount?

A: The slope of the line that represents the reimbursement amount is $0.65$, which represents the reimbursement amount per mile.

Q: What is the y-intercept of the line that represents the reimbursement amount?

A: The y-intercept of the line that represents the reimbursement amount is $145$, which represents the annual maintenance cost.

Q: Can I graph the equation to visualize the reimbursement amount?

A: Yes, you can graph the equation $C = 0.65x + 145$ to visualize the reimbursement amount. The graph will be a straight line with a slope of $0.65$ and a y-intercept of $145$.

Q: How can I interpret the graph of the equation?

A: The graph of the equation $C = 0.65x + 145$ can be interpreted as follows:

• The slope of the line represents the reimbursement amount per mile ($0.65$).
• The y-intercept of the line represents the annual maintenance cost ($145$).

Q: Can I use the equation to calculate the reimbursement amount for any given number of miles driven?

A: Yes, you can use the equation $C = 0.65x + 145$ to calculate the reimbursement amount for any given number of miles driven.

Q: What is the relationship between the equation and the graph?

A: The equation $C = 0.65x + 145$ and the graph of the equation are related in the following way:

• The equation represents the reimbursement amount for the number of miles driven and the annual maintenance cost.
• The graph of the equation represents the relationship between the reimbursement amount and the number of miles driven.

Q: Can I use the equation to compare the reimbursement amounts for different numbers of miles driven?

A: Yes, you can use the equation $C = 0.65x + 145$ to compare the reimbursement amounts for different numbers of miles driven.

Q: How can I use the equation to make predictions about the reimbursement amount?

A: You can use the equation $C = 0.65x + 145$ to make predictions about the reimbursement amount by plugging in different values of $x$ and solving for $C$.