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 = 0.65 + 145x[/tex]

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

C. [tex]C = 65x + 145[/tex]

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

Answer :

Sure! Let's break down the problem step-by-step to understand which equation models the total amount of reimbursement that Donald's company offers.

1. Understand the Reimbursement Structure:
- The company reimburses [tex]$0.65 per mile driven.
- Additionally, there is a fixed reimbursement of $[/tex]145 per year for maintenance.

2. Define the Variables:
- Let [tex]\( x \)[/tex] represent the number of miles driven by Donald.
- Let [tex]\( C \)[/tex] represent the total reimbursement amount.

3. Construct the Equation:
- The reimbursement for the miles driven is calculated by multiplying the cost per mile by the number of miles: [tex]\( 0.65 \times x \)[/tex].
- The total fixed annual maintenance reimbursement is [tex]\( 145 \)[/tex].

4. Combine These Components to Formulate the Total Reimbursement:
- The total reimbursement [tex]\( C \)[/tex] is the sum of the mileage reimbursement and the fixed maintenance amount.
- Therefore, the equation is:
[tex]\[
C = 0.65x + 145
\][/tex]

5. Match With Given Options:
- Let's compare this equation to the provided options:
- Option A: [tex]\( C = 0.65 + 145x \)[/tex]
- Option B: [tex]\( C = 0.65x + 145 \)[/tex]
- Option C: [tex]\( C = 65x + 145 \)[/tex]
- Option D: [tex]\( C = 65 + 145x \)[/tex]

6. Conclusion:
- The correct equation that models the total amount of reimbursement is Option B: [tex]\( C = 0.65x + 145 \)[/tex].

This equation correctly represents the combination of mileage reimbursement and the annual maintenance cost.