Answer :
To determine which equation models the total amount of reimbursement the company offers, let's break down the problem step by step:
1. Understanding the Reimbursement Components:
- The company reimburses at a rate of [tex]$0.45 per mile.
- Additionally, there is a fixed annual maintenance reimbursement of $[/tex]175.
2. Identifying the Representation of Variables:
- Let [tex]\( x \)[/tex] represent the number of miles driven in a year.
3. Creating the Reimbursement Equation:
- The total reimbursement [tex]\( C \)[/tex] will be composed of two parts:
- The mileage reimbursement, which is [tex]$0.45 for each mile, calculated as \( 0.45 \times x \).
- The fixed annual maintenance amount, which is $[/tex]175.
4. Formulating the Total Reimbursement Equation:
- Combine the per-mile cost and the annual fixed cost to model the total reimbursement:
[tex]\[
C = 0.45x + 175
\][/tex]
5. Matching with Given Options:
- The correct equation from the options given is [tex]\( C = 0.45x + 175 \)[/tex].
Therefore, the correct answer is option C: [tex]\( C = 0.45x + 175 \)[/tex].
1. Understanding the Reimbursement Components:
- The company reimburses at a rate of [tex]$0.45 per mile.
- Additionally, there is a fixed annual maintenance reimbursement of $[/tex]175.
2. Identifying the Representation of Variables:
- Let [tex]\( x \)[/tex] represent the number of miles driven in a year.
3. Creating the Reimbursement Equation:
- The total reimbursement [tex]\( C \)[/tex] will be composed of two parts:
- The mileage reimbursement, which is [tex]$0.45 for each mile, calculated as \( 0.45 \times x \).
- The fixed annual maintenance amount, which is $[/tex]175.
4. Formulating the Total Reimbursement Equation:
- Combine the per-mile cost and the annual fixed cost to model the total reimbursement:
[tex]\[
C = 0.45x + 175
\][/tex]
5. Matching with Given Options:
- The correct equation from the options given is [tex]\( C = 0.45x + 175 \)[/tex].
Therefore, the correct answer is option C: [tex]\( C = 0.45x + 175 \)[/tex].
