Answer :
To solve the problem and determine the correct equation for the total amount of reimbursement, we need to understand the components of the reimbursement package.
1. Reimbursement per Mile: The company offers [tex]$0.65 per mile. This means for every mile Donald travels, he gets $[/tex]0.65. If [tex]\( x \)[/tex] represents the number of miles traveled, then the reimbursement for the miles traveled can be expressed as [tex]\( 0.65 \times x \)[/tex].
2. Yearly Maintenance Reimbursement: Additionally, the company provides a fixed reimbursement of $145 each year for maintenance, regardless of the number of miles traveled.
3. Total Reimbursement (C): The total reimbursement [tex]\( C \)[/tex] is the sum of the mileage reimbursement and the yearly maintenance reimbursement. Therefore, the equation that models the total reimbursement can be given by:
[tex]\[
C = 0.65x + 145
\][/tex]
Now, looking at the provided options:
- Option A: [tex]\( C = 0.65x + 145 \)[/tex] is exactly the same as our identified equation for total reimbursement.
- Option B, C, and D: These options do not correctly represent the reimbursement structure as described because they either swap the constant and variable terms or use incorrect coefficients.
Therefore, the correct answer is A. [tex]\( C = 0.65x + 145 \)[/tex].
1. Reimbursement per Mile: The company offers [tex]$0.65 per mile. This means for every mile Donald travels, he gets $[/tex]0.65. If [tex]\( x \)[/tex] represents the number of miles traveled, then the reimbursement for the miles traveled can be expressed as [tex]\( 0.65 \times x \)[/tex].
2. Yearly Maintenance Reimbursement: Additionally, the company provides a fixed reimbursement of $145 each year for maintenance, regardless of the number of miles traveled.
3. Total Reimbursement (C): The total reimbursement [tex]\( C \)[/tex] is the sum of the mileage reimbursement and the yearly maintenance reimbursement. Therefore, the equation that models the total reimbursement can be given by:
[tex]\[
C = 0.65x + 145
\][/tex]
Now, looking at the provided options:
- Option A: [tex]\( C = 0.65x + 145 \)[/tex] is exactly the same as our identified equation for total reimbursement.
- Option B, C, and D: These options do not correctly represent the reimbursement structure as described because they either swap the constant and variable terms or use incorrect coefficients.
Therefore, the correct answer is A. [tex]\( C = 0.65x + 145 \)[/tex].
