Answer :
To solve this problem, we need to determine which equation accurately models the total reimbursement amount, [tex]\( C \)[/tex], that Tim's company offers based on the number of miles, [tex]\( x \)[/tex].
Here's how we can break it down:
1. Understand the reimbursement components:
- The company reimburses [tex]$0.45 per mile. This means for every mile \( x \), there is a compensation of $[/tex]0.45, which can be represented by the term [tex]\( 0.45x \)[/tex].
- Additionally, the company provides an annual maintenance reimbursement of $175. This amount is a fixed cost added to the mileage reimbursement.
2. Formulate the total reimbursement:
- The total reimbursement [tex]\( C \)[/tex] combines both the mileage and the fixed maintenance cost.
- Therefore, the total reimbursement can be expressed as:
[tex]\[
C = 0.45x + 175
\][/tex]
3. Identify the correct equation from the options:
- A. [tex]\( C = 0.45 + 175x \)[/tex]
- B. [tex]\( C = 45x + 175 \)[/tex]
- C. [tex]\( C = 0.45 + 175 \)[/tex]
- D. [tex]\( C = 0.45x + 175 \)[/tex]
From our formulation, we see that option D, [tex]\( C = 0.45x + 175 \)[/tex], correctly represents the company's reimbursement package.
Thus, the correct equation that models the total reimbursement is option D.
Here's how we can break it down:
1. Understand the reimbursement components:
- The company reimburses [tex]$0.45 per mile. This means for every mile \( x \), there is a compensation of $[/tex]0.45, which can be represented by the term [tex]\( 0.45x \)[/tex].
- Additionally, the company provides an annual maintenance reimbursement of $175. This amount is a fixed cost added to the mileage reimbursement.
2. Formulate the total reimbursement:
- The total reimbursement [tex]\( C \)[/tex] combines both the mileage and the fixed maintenance cost.
- Therefore, the total reimbursement can be expressed as:
[tex]\[
C = 0.45x + 175
\][/tex]
3. Identify the correct equation from the options:
- A. [tex]\( C = 0.45 + 175x \)[/tex]
- B. [tex]\( C = 45x + 175 \)[/tex]
- C. [tex]\( C = 0.45 + 175 \)[/tex]
- D. [tex]\( C = 0.45x + 175 \)[/tex]
From our formulation, we see that option D, [tex]\( C = 0.45x + 175 \)[/tex], correctly represents the company's reimbursement package.
Thus, the correct equation that models the total reimbursement is option D.
