Answer :
To solve the problem of determining which equation models the total amount of reimbursement, we need to break down what the reimbursement consists of.
1. Reimbursement Per Mile: Tim's company reimburses [tex]$\$[/tex]0.45[tex]$ for every mile he drives. If Tim drives $[/tex]x[tex]$ miles, the cost for the mileage would be represented by:
\[ 0.45 \times x \]
2. Annual Maintenance Cost: Apart from the mileage reimbursement, Tim’s company also provides a fixed annual maintenance reimbursement of $[/tex]\[tex]$175$[/tex]. This is a constant amount that doesn’t change with the number of miles driven.
3. Total Reimbursement: The total reimbursement package, denoted by [tex]$C$[/tex], would therefore be the sum of the mileage reimbursement and the fixed maintenance reimbursement. This can be mathematically represented as:
[tex]\[ C = 0.45x + 175 \][/tex]
Thus, the correct equation that models the total reimbursement amount is choice C: [tex]$C = 0.45x + 175$[/tex].
1. Reimbursement Per Mile: Tim's company reimburses [tex]$\$[/tex]0.45[tex]$ for every mile he drives. If Tim drives $[/tex]x[tex]$ miles, the cost for the mileage would be represented by:
\[ 0.45 \times x \]
2. Annual Maintenance Cost: Apart from the mileage reimbursement, Tim’s company also provides a fixed annual maintenance reimbursement of $[/tex]\[tex]$175$[/tex]. This is a constant amount that doesn’t change with the number of miles driven.
3. Total Reimbursement: The total reimbursement package, denoted by [tex]$C$[/tex], would therefore be the sum of the mileage reimbursement and the fixed maintenance reimbursement. This can be mathematically represented as:
[tex]\[ C = 0.45x + 175 \][/tex]
Thus, the correct equation that models the total reimbursement amount is choice C: [tex]$C = 0.45x + 175$[/tex].
