Answer :
To determine the correct equation that models the total amount of reimbursement, let's break down the components of the reimbursement package:
1. Reimbursement per mile: The company offers [tex]$0.45 for every mile driven. This means if Tim drives `x` miles, the reimbursement for this portion will be $[/tex]0.45 times `x`, which is represented as `0.45x`.
2. Annual maintenance reimbursement: The company also provides a fixed amount of $175 each year for maintenance.
Now, we need to combine these two components to create the total reimbursement equation:
- The total reimbursement `C` will be the sum of the reimbursement per mile and the annual maintenance cost.
So, the equation that represents the total reimbursement `C` is:
[tex]\[ C = 0.45x + 175 \][/tex]
Upon looking at the options provided:
A. [tex]\( C = 0.45 + 175x \)[/tex] - This option incorrectly places 175 as a coefficient to `x`.
B. [tex]\( C = 0.45x + 175 \)[/tex] - This option represents the correct equation as we derived.
C. [tex]\( C = 45x + 175 \)[/tex] - This option incorrectly uses 45 instead of 0.45 as the coefficient of `x`.
D. [tex]\( C = 0.45 + 175 \)[/tex] - This option ignores the `x` factor for mileage.
Therefore, the correct answer is:
B. [tex]\( C = 0.45x + 175 \)[/tex]
1. Reimbursement per mile: The company offers [tex]$0.45 for every mile driven. This means if Tim drives `x` miles, the reimbursement for this portion will be $[/tex]0.45 times `x`, which is represented as `0.45x`.
2. Annual maintenance reimbursement: The company also provides a fixed amount of $175 each year for maintenance.
Now, we need to combine these two components to create the total reimbursement equation:
- The total reimbursement `C` will be the sum of the reimbursement per mile and the annual maintenance cost.
So, the equation that represents the total reimbursement `C` is:
[tex]\[ C = 0.45x + 175 \][/tex]
Upon looking at the options provided:
A. [tex]\( C = 0.45 + 175x \)[/tex] - This option incorrectly places 175 as a coefficient to `x`.
B. [tex]\( C = 0.45x + 175 \)[/tex] - This option represents the correct equation as we derived.
C. [tex]\( C = 45x + 175 \)[/tex] - This option incorrectly uses 45 instead of 0.45 as the coefficient of `x`.
D. [tex]\( C = 0.45 + 175 \)[/tex] - This option ignores the `x` factor for mileage.
Therefore, the correct answer is:
B. [tex]\( C = 0.45x + 175 \)[/tex]
