Answer :
To solve this problem, we need to determine the equation that models the total amount of reimbursement, [tex]\( C \)[/tex], that Donald's company offers based on the number of miles driven, represented by [tex]\( x \)[/tex].
1. Understand the components of the reimbursement package:
- The company provides a reimbursement of \[tex]$0.65 per mile.
- Additionally, there is a fixed annual maintenance reimbursement of \$[/tex]145.
2. Construct the equation:
- Since the reimbursement per mile depends on how many miles [tex]\( x \)[/tex] are driven, this part of the reimbursement can be represented by [tex]\( 0.65x \)[/tex]. Here, you multiply the number of miles by the reimbursement rate per mile.
- The fixed amount for annual maintenance is a one-time addition of \$145, which does not depend on the number of miles driven.
3. Combine the components:
- To find the total reimbursement [tex]\( C \)[/tex], you add the mileage-based reimbursement to the annual maintenance amount:
[tex]\[
C = 0.65x + 145
\][/tex]
Thus, the correct equation that models the total reimbursement is:
[tex]\[ C = 0.65x + 145 \][/tex]
Looking at the options given, option B corresponds to this equation. Therefore, the correct choice is:
B. [tex]\( C = 0.65x + 145 \)[/tex]
1. Understand the components of the reimbursement package:
- The company provides a reimbursement of \[tex]$0.65 per mile.
- Additionally, there is a fixed annual maintenance reimbursement of \$[/tex]145.
2. Construct the equation:
- Since the reimbursement per mile depends on how many miles [tex]\( x \)[/tex] are driven, this part of the reimbursement can be represented by [tex]\( 0.65x \)[/tex]. Here, you multiply the number of miles by the reimbursement rate per mile.
- The fixed amount for annual maintenance is a one-time addition of \$145, which does not depend on the number of miles driven.
3. Combine the components:
- To find the total reimbursement [tex]\( C \)[/tex], you add the mileage-based reimbursement to the annual maintenance amount:
[tex]\[
C = 0.65x + 145
\][/tex]
Thus, the correct equation that models the total reimbursement is:
[tex]\[ C = 0.65x + 145 \][/tex]
Looking at the options given, option B corresponds to this equation. Therefore, the correct choice is:
B. [tex]\( C = 0.65x + 145 \)[/tex]
