Answer :
Certainly! Let's break down how to determine the correct equation for the total reimbursement, [tex]\( C \)[/tex], that Tim's company offers, based on the number of miles driven, [tex]\( x \)[/tex].
1. Understand the reimbursement breakdown:
- Per Mile Reimbursement: The company reimburses [tex]$0.45 per mile. This part of the reimbursement depends on the number of miles, \( x \), so we represent it as \( 0.45x \).
- Annual Maintenance Cost: Regardless of the miles driven, the company also provides an additional fixed amount of $[/tex]175 per year for maintenance.
2. Combine the costs:
- To find the total reimbursement [tex]\( C \)[/tex], we need to add the mileage reimbursement to the annual maintenance:
- The mileage cost is [tex]\( 0.45x \)[/tex].
- The maintenance cost is $175.
- Therefore, the equation for the total reimbursement [tex]\( C \)[/tex] is:
[tex]\[
C = 0.45x + 175
\][/tex]
3. Compare with the given options:
- Option A: [tex]\( C = 45x + 175 \)[/tex] (incorrect, as it uses 45 instead of 0.45).
- Option B: [tex]\( C = 0.45 + 175 \)[/tex] (incorrect, as it doesn't multiply 0.45 by [tex]\( x \)[/tex]).
- Option C: [tex]\( C = 0.45 + 175x \)[/tex] (incorrect, as it mistakenly applies the annual cost per mile).
- Option D: [tex]\( C = 0.45x + 175 \)[/tex] (correct, this matches our calculated equation).
Thus, the correct equation that models the total amount of reimbursement is [tex]\( C = 0.45x + 175 \)[/tex], which matches Option D.
1. Understand the reimbursement breakdown:
- Per Mile Reimbursement: The company reimburses [tex]$0.45 per mile. This part of the reimbursement depends on the number of miles, \( x \), so we represent it as \( 0.45x \).
- Annual Maintenance Cost: Regardless of the miles driven, the company also provides an additional fixed amount of $[/tex]175 per year for maintenance.
2. Combine the costs:
- To find the total reimbursement [tex]\( C \)[/tex], we need to add the mileage reimbursement to the annual maintenance:
- The mileage cost is [tex]\( 0.45x \)[/tex].
- The maintenance cost is $175.
- Therefore, the equation for the total reimbursement [tex]\( C \)[/tex] is:
[tex]\[
C = 0.45x + 175
\][/tex]
3. Compare with the given options:
- Option A: [tex]\( C = 45x + 175 \)[/tex] (incorrect, as it uses 45 instead of 0.45).
- Option B: [tex]\( C = 0.45 + 175 \)[/tex] (incorrect, as it doesn't multiply 0.45 by [tex]\( x \)[/tex]).
- Option C: [tex]\( C = 0.45 + 175x \)[/tex] (incorrect, as it mistakenly applies the annual cost per mile).
- Option D: [tex]\( C = 0.45x + 175 \)[/tex] (correct, this matches our calculated equation).
Thus, the correct equation that models the total amount of reimbursement is [tex]\( C = 0.45x + 175 \)[/tex], which matches Option D.
