Answer :
To figure out the correct equation for the total amount of reimbursement, we need to consider both components of the company's reimbursement package:
1. Per Mile Reimbursement: Joseph's company offers a reimbursement of [tex]$0.45 for each mile driven. If Joseph drives \(x\) miles, the total reimbursement for the miles is \(0.45 \times x\).
2. Annual Maintenance Reimbursement: In addition to the per mile reimbursement, there's a flat rate of $[/tex]175 given annually for maintenance. This does not depend on the number of miles driven.
Given these two components, the total reimbursement [tex]\(C\)[/tex] combines both the mileage reimbursement and the maintenance fee. So, the equation to model this situation is:
[tex]\[ C = 0.45x + 175 \][/tex]
This represents the total cost ([tex]\(C\)[/tex]) as the sum of the reimbursement for the miles driven and the annual maintenance payment.
Reviewing the options provided:
- Option A: [tex]\(C = 45x + 175\)[/tex]
- Option B: [tex]\(C = 45 + 175x\)[/tex]
- Option C: [tex]\(C = 0.45 + 175x\)[/tex]
- Option D: [tex]\(C = 0.45x + 175\)[/tex]
The correct equation is option D: [tex]\(C = 0.45x + 175\)[/tex], which accurately represents the total reimbursement based on the number of miles driven and the fixed annual maintenance fee.
1. Per Mile Reimbursement: Joseph's company offers a reimbursement of [tex]$0.45 for each mile driven. If Joseph drives \(x\) miles, the total reimbursement for the miles is \(0.45 \times x\).
2. Annual Maintenance Reimbursement: In addition to the per mile reimbursement, there's a flat rate of $[/tex]175 given annually for maintenance. This does not depend on the number of miles driven.
Given these two components, the total reimbursement [tex]\(C\)[/tex] combines both the mileage reimbursement and the maintenance fee. So, the equation to model this situation is:
[tex]\[ C = 0.45x + 175 \][/tex]
This represents the total cost ([tex]\(C\)[/tex]) as the sum of the reimbursement for the miles driven and the annual maintenance payment.
Reviewing the options provided:
- Option A: [tex]\(C = 45x + 175\)[/tex]
- Option B: [tex]\(C = 45 + 175x\)[/tex]
- Option C: [tex]\(C = 0.45 + 175x\)[/tex]
- Option D: [tex]\(C = 0.45x + 175\)[/tex]
The correct equation is option D: [tex]\(C = 0.45x + 175\)[/tex], which accurately represents the total reimbursement based on the number of miles driven and the fixed annual maintenance fee.
