Answer :
To solve the problem, we need to find the correct equation that models the total amount of reimbursement, [tex]\( C \)[/tex], the company offers based on the number of miles driven, [tex]\( x \)[/tex].
1. Understand the Reimbursement Components:
- The company reimburses [tex]$0.45 per mile driven.
- Additionally, the company provides a fixed amount of $[/tex]175 per year for maintenance.
2. Develop the Equation:
- The total reimbursement [tex]\( C \)[/tex] consists of two parts:
- A variable part that depends on the number of miles driven: [tex]\( 0.45 \times x \)[/tex], where [tex]\( x \)[/tex] is the number of miles.
- A fixed part that is given annually as [tex]$175.
3. Combine the Components:
- To model the total reimbursement \( C \), you add the variable part and the fixed part together:
\[
C = 0.45x + 175
\]
4. Identify the Correct Option:
- Option A: \( C = 0.45 + 175 \) - Incorrect, as it lacks the multiplication by \( x \) representing the miles.
- Option B: \( C = 0.45 + 175x \) - Incorrect, as it improperly multiplies the fixed amount by the miles.
- Option C: \( C = 45x + 175 \) - Incorrect, because the cost per mile should be $[/tex]0.45, not $45.
- Option D: [tex]\( C = 0.45x + 175 \)[/tex] - Correct, as it properly models the reimbursement by considering both the per mile variable component and the fixed annual component.
Thus, the correct equation that models the total reimbursement is [tex]\( C = 0.45x + 175 \)[/tex]. Therefore, the answer is option D.
1. Understand the Reimbursement Components:
- The company reimburses [tex]$0.45 per mile driven.
- Additionally, the company provides a fixed amount of $[/tex]175 per year for maintenance.
2. Develop the Equation:
- The total reimbursement [tex]\( C \)[/tex] consists of two parts:
- A variable part that depends on the number of miles driven: [tex]\( 0.45 \times x \)[/tex], where [tex]\( x \)[/tex] is the number of miles.
- A fixed part that is given annually as [tex]$175.
3. Combine the Components:
- To model the total reimbursement \( C \), you add the variable part and the fixed part together:
\[
C = 0.45x + 175
\]
4. Identify the Correct Option:
- Option A: \( C = 0.45 + 175 \) - Incorrect, as it lacks the multiplication by \( x \) representing the miles.
- Option B: \( C = 0.45 + 175x \) - Incorrect, as it improperly multiplies the fixed amount by the miles.
- Option C: \( C = 45x + 175 \) - Incorrect, because the cost per mile should be $[/tex]0.45, not $45.
- Option D: [tex]\( C = 0.45x + 175 \)[/tex] - Correct, as it properly models the reimbursement by considering both the per mile variable component and the fixed annual component.
Thus, the correct equation that models the total reimbursement is [tex]\( C = 0.45x + 175 \)[/tex]. Therefore, the answer is option D.
