Answer :
To solve this problem, we need to find an equation that models the total amount of reimbursement, [tex]\( C \)[/tex], that Tim's company offers. The reimbursement is based on two components:
1. A variable component of [tex]\(\$0.45\)[/tex] per mile.
2. A fixed annual maintenance reimbursement of [tex]\(\$175\)[/tex].
We can represent the total reimbursement [tex]\( C \)[/tex] with the number of miles [tex]\( x \)[/tex].
Here's how we set up the equation:
1. Variable Reimbursement: Since the company reimburses [tex]\(\$0.45\)[/tex] for each mile, the total reimbursement for mileage can be expressed as [tex]\( 0.45 \times x \)[/tex], where [tex]\( x \)[/tex] is the number of miles.
2. Fixed Reimbursement: The company also provides a fixed reimbursement of [tex]\(\$175\)[/tex] for maintenance for the entire year. This value stays constant regardless of the miles driven.
3. Total Reimbursement Equation: To find the total reimbursement, we add the variable reimbursement to the fixed annual maintenance. Therefore, the equation is:
[tex]\[
C = 0.45x + 175
\][/tex]
Now, let's compare this with the provided options. The correct equation is:
A. [tex]\( C = 0.45x + 175 \)[/tex]
This equation matches the model we developed based on the reimbursement package provided by Tim's company.
1. A variable component of [tex]\(\$0.45\)[/tex] per mile.
2. A fixed annual maintenance reimbursement of [tex]\(\$175\)[/tex].
We can represent the total reimbursement [tex]\( C \)[/tex] with the number of miles [tex]\( x \)[/tex].
Here's how we set up the equation:
1. Variable Reimbursement: Since the company reimburses [tex]\(\$0.45\)[/tex] for each mile, the total reimbursement for mileage can be expressed as [tex]\( 0.45 \times x \)[/tex], where [tex]\( x \)[/tex] is the number of miles.
2. Fixed Reimbursement: The company also provides a fixed reimbursement of [tex]\(\$175\)[/tex] for maintenance for the entire year. This value stays constant regardless of the miles driven.
3. Total Reimbursement Equation: To find the total reimbursement, we add the variable reimbursement to the fixed annual maintenance. Therefore, the equation is:
[tex]\[
C = 0.45x + 175
\][/tex]
Now, let's compare this with the provided options. The correct equation is:
A. [tex]\( C = 0.45x + 175 \)[/tex]
This equation matches the model we developed based on the reimbursement package provided by Tim's company.
