Answer :
To solve the problem of finding the correct equation that models the total reimbursement amount [tex]\( C \)[/tex] for Joseph's company, we need to carefully analyze the information given:
1. Reimbursement Rate per Mile: The company offers a reimbursement of \[tex]$0.45 per mile driven. If Joseph drives \( x \) miles, the total reimbursement for mileage would be calculated as:
\[
0.45 \times x
\]
2. Annual Maintenance Reimbursement: In addition to the mileage reimbursement, the company offers a flat amount of \$[/tex]175 per year for maintenance. This is a constant amount that does not depend on the number of miles driven.
3. Total Reimbursement [tex]\( C \)[/tex]: To find the total reimbursement [tex]\( C \)[/tex], we need to add both the reimbursement for the miles driven and the annual maintenance reimbursement. Therefore, the equation for the total reimbursement will be:
[tex]\[
C = 0.45 \times x + 175
\][/tex]
Now, let's match this equation to the options given:
- Option A: [tex]\( C = 0.45x + 175 \)[/tex]
- Option B: [tex]\( C = 45 + 175x \)[/tex]
- Option C: [tex]\( C = 45x + 175 \)[/tex]
- Option D: [tex]\( C = 0.45 + 175x \)[/tex]
The equation [tex]\( C = 0.45x + 175 \)[/tex] matches Option A.
Therefore, the correct equation that models the total reimbursement offered by Joseph's company is:
Option A: [tex]\( C = 0.45x + 175 \)[/tex].
1. Reimbursement Rate per Mile: The company offers a reimbursement of \[tex]$0.45 per mile driven. If Joseph drives \( x \) miles, the total reimbursement for mileage would be calculated as:
\[
0.45 \times x
\]
2. Annual Maintenance Reimbursement: In addition to the mileage reimbursement, the company offers a flat amount of \$[/tex]175 per year for maintenance. This is a constant amount that does not depend on the number of miles driven.
3. Total Reimbursement [tex]\( C \)[/tex]: To find the total reimbursement [tex]\( C \)[/tex], we need to add both the reimbursement for the miles driven and the annual maintenance reimbursement. Therefore, the equation for the total reimbursement will be:
[tex]\[
C = 0.45 \times x + 175
\][/tex]
Now, let's match this equation to the options given:
- Option A: [tex]\( C = 0.45x + 175 \)[/tex]
- Option B: [tex]\( C = 45 + 175x \)[/tex]
- Option C: [tex]\( C = 45x + 175 \)[/tex]
- Option D: [tex]\( C = 0.45 + 175x \)[/tex]
The equation [tex]\( C = 0.45x + 175 \)[/tex] matches Option A.
Therefore, the correct equation that models the total reimbursement offered by Joseph's company is:
Option A: [tex]\( C = 0.45x + 175 \)[/tex].
