High School

Donald's company offers a reimbursement package of [tex]\$0.65[/tex] per mile plus [tex]\$145[/tex] a year for maintenance. If [tex]x[/tex] represents the number of miles, which equation below models [tex]C[/tex], the total amount of reimbursement the company offers?

A. [tex]C = 65x + 145[/tex]
B. [tex]C = 0.65x + 145[/tex]
C. [tex]C = 65 + 145x[/tex]
D. [tex]C = 0.65 + 145x[/tex]

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]