Answer :
To solve the problem of determining which equation correctly models the total amount of reimbursement the company offers, we need to understand the components of the reimbursement package:
1. Mileage Reimbursement: The company offers [tex]$0.45 per mile. This means that for every mile driven, an employee is reimbursed $[/tex]0.45. If [tex]\( x \)[/tex] represents the number of miles driven, the reimbursement for mileage is [tex]\( 0.45x \)[/tex].
2. Annual Maintenance Fee: Additionally, the company provides a flat amount of [tex]$175 per year for maintenance. This is a constant amount that does not depend on the number of miles driven.
To find the total reimbursement \( C \), we add together both the mileage reimbursement and the annual maintenance fee. Therefore, the expression that models this is:
\[ C = 0.45x + 175 \]
Now, let's analyze each of the options given to identify the correct one:
A. \( C = 0.45 + 175x \): This option incorrectly adds $[/tex]0.45 directly to [tex]\( 175x \)[/tex], which is not appropriate since [tex]$0.45 should be multiplied by the miles (\( x \)).
B. \( C = 0.45 + 175 \): This option doesn't account for the number of miles driven, thus it doesn't include the variable \( x \), which makes it incorrect.
C. \( C = 0.45x + 175 \): This option correctly models the reimbursement by multiplying $[/tex]0.45 by the miles ([tex]\( x \)[/tex]), then adding the [tex]$175 annual maintenance fee.
D. \( C = 45x + 175 \): This option uses $[/tex]45 per mile instead of $0.45, which is not correct.
Thus, the correct equation that models the total reimbursement is option C:
[tex]\[ C = 0.45x + 175 \][/tex]
1. Mileage Reimbursement: The company offers [tex]$0.45 per mile. This means that for every mile driven, an employee is reimbursed $[/tex]0.45. If [tex]\( x \)[/tex] represents the number of miles driven, the reimbursement for mileage is [tex]\( 0.45x \)[/tex].
2. Annual Maintenance Fee: Additionally, the company provides a flat amount of [tex]$175 per year for maintenance. This is a constant amount that does not depend on the number of miles driven.
To find the total reimbursement \( C \), we add together both the mileage reimbursement and the annual maintenance fee. Therefore, the expression that models this is:
\[ C = 0.45x + 175 \]
Now, let's analyze each of the options given to identify the correct one:
A. \( C = 0.45 + 175x \): This option incorrectly adds $[/tex]0.45 directly to [tex]\( 175x \)[/tex], which is not appropriate since [tex]$0.45 should be multiplied by the miles (\( x \)).
B. \( C = 0.45 + 175 \): This option doesn't account for the number of miles driven, thus it doesn't include the variable \( x \), which makes it incorrect.
C. \( C = 0.45x + 175 \): This option correctly models the reimbursement by multiplying $[/tex]0.45 by the miles ([tex]\( x \)[/tex]), then adding the [tex]$175 annual maintenance fee.
D. \( C = 45x + 175 \): This option uses $[/tex]45 per mile instead of $0.45, which is not correct.
Thus, the correct equation that models the total reimbursement is option C:
[tex]\[ C = 0.45x + 175 \][/tex]
