Answer :
To determine the correct equation for Tim's company's reimbursement package, we need to consider both parts of the package: the reimbursement per mile driven and the yearly maintenance fee.
1. Reimbursement Per Mile:
- The company reimburses [tex]$0.45 per mile. This means if Tim drives \( x \) miles, the reimbursement would be \( 0.45 \times x \).
2. Yearly Maintenance Fee:
- In addition to the mileage reimbursement, the company also provides a flat maintenance fee of $[/tex]175 per year.
Combining both the mileage reimbursement and the maintenance fee, the total amount of reimbursement [tex]\( C \)[/tex] can be calculated with the equation:
[tex]\[ C = 0.45x + 175 \][/tex]
Now, let's match this equation with the given choices:
A. [tex]\( C = 45x + 175 \)[/tex]
- This is incorrect because the reimbursement per mile is [tex]$0.45, not $[/tex]45.
B. [tex]\( C = 0.45 + 175 \)[/tex]
- This is incorrect because it does not account for the variable [tex]\( x \)[/tex], the number of miles driven.
C. [tex]\( C = 0.45x + 175 \)[/tex]
- This is correct because it accurately represents the total reimbursement as the sum of the mileage and the maintenance fee.
D. [tex]\( C = 0.45 + 175x \)[/tex]
- This is incorrect because the [tex]$0.45 should be multiplied by the number of miles \( x \), not added directly to $[/tex]175 times [tex]\( x \)[/tex].
Thus, option C, [tex]\( C = 0.45x + 175 \)[/tex], is the correct equation that models the total reimbursement offered by the company.
1. Reimbursement Per Mile:
- The company reimburses [tex]$0.45 per mile. This means if Tim drives \( x \) miles, the reimbursement would be \( 0.45 \times x \).
2. Yearly Maintenance Fee:
- In addition to the mileage reimbursement, the company also provides a flat maintenance fee of $[/tex]175 per year.
Combining both the mileage reimbursement and the maintenance fee, the total amount of reimbursement [tex]\( C \)[/tex] can be calculated with the equation:
[tex]\[ C = 0.45x + 175 \][/tex]
Now, let's match this equation with the given choices:
A. [tex]\( C = 45x + 175 \)[/tex]
- This is incorrect because the reimbursement per mile is [tex]$0.45, not $[/tex]45.
B. [tex]\( C = 0.45 + 175 \)[/tex]
- This is incorrect because it does not account for the variable [tex]\( x \)[/tex], the number of miles driven.
C. [tex]\( C = 0.45x + 175 \)[/tex]
- This is correct because it accurately represents the total reimbursement as the sum of the mileage and the maintenance fee.
D. [tex]\( C = 0.45 + 175x \)[/tex]
- This is incorrect because the [tex]$0.45 should be multiplied by the number of miles \( x \), not added directly to $[/tex]175 times [tex]\( x \)[/tex].
Thus, option C, [tex]\( C = 0.45x + 175 \)[/tex], is the correct equation that models the total reimbursement offered by the company.
