Answer :
To solve the problem, we need to find the correct mathematical equation that models the total amount of reimbursement, [tex]\( C \)[/tex], that Tim's company offers for driving [tex]\( x \)[/tex] miles.
According to the problem, the reimbursement package includes:
1. A rate of [tex]$0.45 per mile.
2. A fixed maintenance cost of $[/tex]175 per year.
The total reimbursement [tex]\( C \)[/tex] can be calculated by taking the reimbursement per mile and multiplying it by the number of miles driven, and then adding the fixed maintenance cost.
Let's break down the components:
- For the mileage component:
- The reimbursement rate is [tex]$0.45 per mile.
- If \( x \) is the number of miles, the total reimbursement for mileage is \( 0.45 \times x \).
- For the maintenance component:
- There is a fixed cost of $[/tex]175.
Thus, the equation that models the total reimbursement [tex]\( C \)[/tex] is:
[tex]\[ C = 0.45x + 175 \][/tex]
Now, let's match this equation to the options provided:
- Option A: [tex]\( C = 0.45x + 175 \)[/tex]
- Option B: [tex]\( C = 0.45 + 175 \)[/tex]
- Option C: [tex]\( C = 0.45 + 175x \)[/tex]
- Option D: [tex]\( C = 45x + 175 \)[/tex]
The equation [tex]\( C = 0.45x + 175 \)[/tex] matches Option A.
Therefore, the correct option is A.
According to the problem, the reimbursement package includes:
1. A rate of [tex]$0.45 per mile.
2. A fixed maintenance cost of $[/tex]175 per year.
The total reimbursement [tex]\( C \)[/tex] can be calculated by taking the reimbursement per mile and multiplying it by the number of miles driven, and then adding the fixed maintenance cost.
Let's break down the components:
- For the mileage component:
- The reimbursement rate is [tex]$0.45 per mile.
- If \( x \) is the number of miles, the total reimbursement for mileage is \( 0.45 \times x \).
- For the maintenance component:
- There is a fixed cost of $[/tex]175.
Thus, the equation that models the total reimbursement [tex]\( C \)[/tex] is:
[tex]\[ C = 0.45x + 175 \][/tex]
Now, let's match this equation to the options provided:
- Option A: [tex]\( C = 0.45x + 175 \)[/tex]
- Option B: [tex]\( C = 0.45 + 175 \)[/tex]
- Option C: [tex]\( C = 0.45 + 175x \)[/tex]
- Option D: [tex]\( C = 45x + 175 \)[/tex]
The equation [tex]\( C = 0.45x + 175 \)[/tex] matches Option A.
Therefore, the correct option is A.
