Answer :
To solve the problem, let's break it down step-by-step:
1. Understanding the Reimbursement Package:
- Tim's company offers two components for reimbursement:
- [tex]$0.45 per mile driven.
- A fixed amount of $[/tex]175 per year for maintenance.
2. Translating the Information to a Mathematical Model:
- Let [tex]\( x \)[/tex] represent the number of miles driven.
- The reimbursement for the mileage is calculated as [tex]\( 0.45 \times x \)[/tex], which represents [tex]$0.45 per mile.
- Additionally, the $[/tex]175 is a fixed annual reimbursement for maintenance.
3. Formulating the Equation for Total Reimbursement ([tex]\( C \)[/tex]):
- The total reimbursement [tex]\( C \)[/tex] is the sum of the mileage reimbursement and the maintenance reimbursement. This can be expressed as:
[tex]\[
C = 0.45x + 175
\][/tex]
4. Selecting the Correct Equation from the Given Options:
Let's compare this equation with the options provided:
- A. [tex]\( C = 0.45 + 175 \)[/tex]
- B. [tex]\( C = 0.45x + 175 \)[/tex]
- C. [tex]\( C = 45x + 175 \)[/tex]
- D. [tex]\( C = 0.45 + 175x \)[/tex]
The correct equation is B: [tex]\( C = 0.45x + 175 \)[/tex] because it correctly models the cost per mile ([tex]\( 0.45x \)[/tex]) and adds the fixed maintenance cost ($175).
Therefore, the correct answer is B.
1. Understanding the Reimbursement Package:
- Tim's company offers two components for reimbursement:
- [tex]$0.45 per mile driven.
- A fixed amount of $[/tex]175 per year for maintenance.
2. Translating the Information to a Mathematical Model:
- Let [tex]\( x \)[/tex] represent the number of miles driven.
- The reimbursement for the mileage is calculated as [tex]\( 0.45 \times x \)[/tex], which represents [tex]$0.45 per mile.
- Additionally, the $[/tex]175 is a fixed annual reimbursement for maintenance.
3. Formulating the Equation for Total Reimbursement ([tex]\( C \)[/tex]):
- The total reimbursement [tex]\( C \)[/tex] is the sum of the mileage reimbursement and the maintenance reimbursement. This can be expressed as:
[tex]\[
C = 0.45x + 175
\][/tex]
4. Selecting the Correct Equation from the Given Options:
Let's compare this equation with the options provided:
- A. [tex]\( C = 0.45 + 175 \)[/tex]
- B. [tex]\( C = 0.45x + 175 \)[/tex]
- C. [tex]\( C = 45x + 175 \)[/tex]
- D. [tex]\( C = 0.45 + 175x \)[/tex]
The correct equation is B: [tex]\( C = 0.45x + 175 \)[/tex] because it correctly models the cost per mile ([tex]\( 0.45x \)[/tex]) and adds the fixed maintenance cost ($175).
Therefore, the correct answer is B.
