Answer :
To solve this problem, we need to find the correct equation that models the total amount of reimbursement, [tex]\( C \)[/tex], a company offers based on the number of miles, [tex]\( x \)[/tex].
Here's how to understand the problem:
1. Reimbursement Per Mile: The company reimburses [tex]$0.45 per mile. This means for every mile driven, the reimbursement increases by $[/tex]0.45. If [tex]\( x \)[/tex] represents the number of miles, then the reimbursement for mileage would be [tex]$0.45 times \( x \). So, the part of the equation that represents this is \( 0.45x \).
2. Annual Maintenance Reimbursement: In addition to the mileage reimbursement, the company offers a flat rate of $[/tex]175 per year for maintenance. This is a constant amount added to the reimbursement total each year. This part of the equation is just $175.
3. Total Reimbursement Equation: To find the total reimbursement, you combine the reimbursement for mileage and the flat maintenance fee. This means you add the amount from the mileage equation to the maintenance fee.
Putting both parts together, the total reimbursement [tex]\( C \)[/tex] is given by:
[tex]\[ C = 0.45x + 175 \][/tex]
Therefore, the correct equation that models the total amount of reimbursement is:
D. [tex]\( C = 0.45x + 175 \)[/tex].
Here's how to understand the problem:
1. Reimbursement Per Mile: The company reimburses [tex]$0.45 per mile. This means for every mile driven, the reimbursement increases by $[/tex]0.45. If [tex]\( x \)[/tex] represents the number of miles, then the reimbursement for mileage would be [tex]$0.45 times \( x \). So, the part of the equation that represents this is \( 0.45x \).
2. Annual Maintenance Reimbursement: In addition to the mileage reimbursement, the company offers a flat rate of $[/tex]175 per year for maintenance. This is a constant amount added to the reimbursement total each year. This part of the equation is just $175.
3. Total Reimbursement Equation: To find the total reimbursement, you combine the reimbursement for mileage and the flat maintenance fee. This means you add the amount from the mileage equation to the maintenance fee.
Putting both parts together, the total reimbursement [tex]\( C \)[/tex] is given by:
[tex]\[ C = 0.45x + 175 \][/tex]
Therefore, the correct equation that models the total amount of reimbursement is:
D. [tex]\( C = 0.45x + 175 \)[/tex].
