Answer :
Certainly! Let's figure out which equation models the total reimbursement, [tex]\( C \)[/tex], that Tim's company offers:
1. Reimbursement Per Mile:
The company offers \[tex]$0.45 for each mile driven. If \( x \) represents the number of miles, the reimbursement for the miles is calculated as:
\[
0.45 \times x
\]
2. Fixed Maintenance Fee:
In addition to the mileage reimbursement, Tim's company also pays a fixed amount of \$[/tex]175 per year for maintenance. This adds a constant value to the total reimbursement.
3. Total Reimbursement Model:
The total reimbursement, [tex]\( C \)[/tex], is the sum of the reimbursement per mile and the fixed maintenance fee:
[tex]\[
C = 0.45x + 175
\][/tex]
Now, let's match this model to the given options:
- A. [tex]\( C = 45x + 175 \)[/tex] – This option incorrectly calculates the per-mile reimbursement.
- B. [tex]\( C = 0.45 + 175x \)[/tex] – This option incorrectly applies the 0.45 factor and the 175 value.
- C. [tex]\( C = 0.45 + 175 \)[/tex] – This option doesn't account for the variable nature of miles.
- D. [tex]\( C = 0.45x + 175 \)[/tex] – This correctly represents the total reimbursement, with 0.45 per mile and an additional 175 fixed amount.
Thus, the correct equation that models the total reimbursement is option D:
[tex]\( C = 0.45x + 175 \)[/tex]
1. Reimbursement Per Mile:
The company offers \[tex]$0.45 for each mile driven. If \( x \) represents the number of miles, the reimbursement for the miles is calculated as:
\[
0.45 \times x
\]
2. Fixed Maintenance Fee:
In addition to the mileage reimbursement, Tim's company also pays a fixed amount of \$[/tex]175 per year for maintenance. This adds a constant value to the total reimbursement.
3. Total Reimbursement Model:
The total reimbursement, [tex]\( C \)[/tex], is the sum of the reimbursement per mile and the fixed maintenance fee:
[tex]\[
C = 0.45x + 175
\][/tex]
Now, let's match this model to the given options:
- A. [tex]\( C = 45x + 175 \)[/tex] – This option incorrectly calculates the per-mile reimbursement.
- B. [tex]\( C = 0.45 + 175x \)[/tex] – This option incorrectly applies the 0.45 factor and the 175 value.
- C. [tex]\( C = 0.45 + 175 \)[/tex] – This option doesn't account for the variable nature of miles.
- D. [tex]\( C = 0.45x + 175 \)[/tex] – This correctly represents the total reimbursement, with 0.45 per mile and an additional 175 fixed amount.
Thus, the correct equation that models the total reimbursement is option D:
[tex]\( C = 0.45x + 175 \)[/tex]
