Answer :
To determine which equation models the total amount of reimbursement that Tim's company offers, we need to consider the components of the reimbursement package:
1. Reimbursement per mile: Tim's company reimburses [tex]$0.45 for every mile driven. If \( x \) represents the number of miles driven, then the reimbursement for miles driven can be calculated as \( 0.45x \).
2. Annual maintenance reimbursement: The company also provides a flat reimbursement of $[/tex]175 per year for maintenance, regardless of the number of miles driven.
To calculate the total amount of reimbursement [tex]\( C \)[/tex], we need to combine the per-mile reimbursement with the fixed annual maintenance reimbursement. The total reimbursement is, therefore, the sum of these two components:
[tex]\[
C = 0.45x + 175
\][/tex]
Let's review the choices given:
- A. [tex]\( C = 0.45 + 175 \)[/tex]
- B. [tex]\( C = 45x + 175 \)[/tex]
- C. [tex]\( C = 0.45 + 175x \)[/tex]
- D. [tex]\( C = 0.45x + 175 \)[/tex]
The correct equation, based on our calculations, is:
- D. [tex]\( C = 0.45x + 175 \)[/tex]
This equation properly models the reimbursement as it includes [tex]$0.45 per mile multiplied by the number of miles and adds the $[/tex]175 maintenance reimbursement.
1. Reimbursement per mile: Tim's company reimburses [tex]$0.45 for every mile driven. If \( x \) represents the number of miles driven, then the reimbursement for miles driven can be calculated as \( 0.45x \).
2. Annual maintenance reimbursement: The company also provides a flat reimbursement of $[/tex]175 per year for maintenance, regardless of the number of miles driven.
To calculate the total amount of reimbursement [tex]\( C \)[/tex], we need to combine the per-mile reimbursement with the fixed annual maintenance reimbursement. The total reimbursement is, therefore, the sum of these two components:
[tex]\[
C = 0.45x + 175
\][/tex]
Let's review the choices given:
- A. [tex]\( C = 0.45 + 175 \)[/tex]
- B. [tex]\( C = 45x + 175 \)[/tex]
- C. [tex]\( C = 0.45 + 175x \)[/tex]
- D. [tex]\( C = 0.45x + 175 \)[/tex]
The correct equation, based on our calculations, is:
- D. [tex]\( C = 0.45x + 175 \)[/tex]
This equation properly models the reimbursement as it includes [tex]$0.45 per mile multiplied by the number of miles and adds the $[/tex]175 maintenance reimbursement.
