Answer :
To solve the problem of finding the correct equation that models the total amount of reimbursement the company offers, we need to understand the components involved:
1. Reimbursement per mile: The company reimburses Tim at a rate of [tex]$0.45 per mile. If \( x \) represents the number of miles, then this part of the reimbursement is represented by \( 0.45x \).
2. Yearly maintenance reimbursement: Additionally, the company provides a $[/tex]175 reimbursement per year for maintenance, which is a constant and does not depend on the number of miles driven.
3. Total reimbursement [tex]\( C \)[/tex]: Therefore, the total reimbursement [tex]\( C \)[/tex] is the sum of the mileage reimbursement and the yearly maintenance. We can model this with the equation [tex]\( C = 0.45x + 175 \)[/tex].
Now, let's match this with the given options:
- Option A: [tex]\( C = 0.45 + 175 \)[/tex]
- This doesn't include the variable [tex]\( x \)[/tex] for miles, and thus it does not appropriately model the reimbursement based on distance traveled.
- Option B: [tex]\( C = 45x + 175 \)[/tex]
- This uses an incorrect rate of 45 instead of 0.45, which inflates the reimbursement per mile by a factor of 100.
- Option C: [tex]\( C = 0.45x + 175 \)[/tex]
- This matches our equation exactly, using the correct rate per mile and adding the yearly maintenance reimbursement.
- Option D: [tex]\( C = 0.45 + 175x \)[/tex]
- This places the $175 as a rate per mile, which is incorrect.
Therefore, the correct option that matches the reimbursement model is Option C: [tex]\( C = 0.45x + 175 \)[/tex].
1. Reimbursement per mile: The company reimburses Tim at a rate of [tex]$0.45 per mile. If \( x \) represents the number of miles, then this part of the reimbursement is represented by \( 0.45x \).
2. Yearly maintenance reimbursement: Additionally, the company provides a $[/tex]175 reimbursement per year for maintenance, which is a constant and does not depend on the number of miles driven.
3. Total reimbursement [tex]\( C \)[/tex]: Therefore, the total reimbursement [tex]\( C \)[/tex] is the sum of the mileage reimbursement and the yearly maintenance. We can model this with the equation [tex]\( C = 0.45x + 175 \)[/tex].
Now, let's match this with the given options:
- Option A: [tex]\( C = 0.45 + 175 \)[/tex]
- This doesn't include the variable [tex]\( x \)[/tex] for miles, and thus it does not appropriately model the reimbursement based on distance traveled.
- Option B: [tex]\( C = 45x + 175 \)[/tex]
- This uses an incorrect rate of 45 instead of 0.45, which inflates the reimbursement per mile by a factor of 100.
- Option C: [tex]\( C = 0.45x + 175 \)[/tex]
- This matches our equation exactly, using the correct rate per mile and adding the yearly maintenance reimbursement.
- Option D: [tex]\( C = 0.45 + 175x \)[/tex]
- This places the $175 as a rate per mile, which is incorrect.
Therefore, the correct option that matches the reimbursement model is Option C: [tex]\( C = 0.45x + 175 \)[/tex].
