To find the correct equation that models the total amount of reimbursement [tex]\( C \)[/tex] that Tim's company offers based on the number of miles driven [tex]\( x \)[/tex], we need to take into account both the per-mile reimbursement rate and the fixed annual maintenance cost.
Let's break down the components of the reimbursement package:
1. Per-Mile Reimbursement:
Tim's company reimburses at a rate of [tex]\( \$0.45 \)[/tex] per mile. If [tex]\( x \)[/tex] represents the number of miles driven, the total reimbursement for mileage would be:
[tex]\[
0.45x
\][/tex]
2. Annual Maintenance Reimbursement:
In addition to the per-mile reimbursement, the company provides a fixed amount of [tex]\( \$175 \)[/tex] per year for maintenance.
To combine both parts, we sum the per-mile reimbursement and the annual maintenance reimbursement to get the total reimbursement [tex]\( C \)[/tex]:
[tex]\[
C = 0.45x + 175
\][/tex]
Now, let's compare this with the provided options:
A. [tex]\[ C = 0.45x + 175 \][/tex]
B. [tex]\[ C = 45x + 175 \][/tex]
C. [tex]\[ C = 0.45 + 175 \][/tex]
D. [tex]\[ C = 0.45 + 175x \][/tex]
Clearly, Option A, [tex]\[ C = 0.45x + 175 \][/tex], accurately represents the total reimbursement [tex]\( C \)[/tex] based on the given reimbursement package, where [tex]\( 0.45 \)[/tex] is the per-mile rate and [tex]\( 175 \)[/tex] is the fixed annual maintenance.
Therefore, the correct equation is:
[tex]\[ \boxed{A. \ C = 0.45x + 175} \][/tex]
