Tim's company offers a reimbursement package of [tex]$\$[/tex]0.45[tex]$ per mile plus $[/tex]\[tex]$175$[/tex] a year for maintenance. If [tex]$x$[/tex] represents the number of miles, which equation below models [tex]$C$[/tex], the total amount of reimbursement the company offers?

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]



Answer :

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]