Answer :
To solve this problem, we are trying to find the correct equation that represents the total amount of reimbursement, [tex]\( C \)[/tex], offered by Tim's company.
Here’s a step-by-step breakdown:
1. Understand the reimbursement model:
- The company offers a reimbursement of [tex]$0.45 per mile.
- Additionally, there is a fixed maintenance reimbursement of $[/tex]175 per year.
2. Define the variable:
- Let [tex]\( x \)[/tex] represent the number of miles driven.
3. Write the equation:
- Since [tex]$0.45 is reimbursed for each mile, the term for mileage reimbursement is \( 0.45x \).
- The $[/tex]175 is a fixed amount added to the mileage reimbursement, regardless of miles driven.
4. Combine to form the total reimbursement equation:
- The total reimbursement, [tex]\( C \)[/tex], is the sum of the mileage reimbursement and the fixed maintenance amount:
[tex]\[
C = 0.45x + 175
\][/tex]
5. Choose the correct option:
- Look at the given options:
- A. [tex]\( C = 45x + 175 \)[/tex]
- B. [tex]\( C = 0.45 + 175 \)[/tex]
- C. [tex]\( C = 0.45x + 175 \)[/tex]
- D. [tex]\( C = 0.45 + 175x \)[/tex]
- The correct equation is:
[tex]\[
C = 0.45x + 175
\][/tex]
- So, the correct choice is option C.
This equation effectively models how the total reimbursement varies with the number of miles driven, incorporating both the variable mileage component and the fixed maintenance component.
Here’s a step-by-step breakdown:
1. Understand the reimbursement model:
- The company offers a reimbursement of [tex]$0.45 per mile.
- Additionally, there is a fixed maintenance reimbursement of $[/tex]175 per year.
2. Define the variable:
- Let [tex]\( x \)[/tex] represent the number of miles driven.
3. Write the equation:
- Since [tex]$0.45 is reimbursed for each mile, the term for mileage reimbursement is \( 0.45x \).
- The $[/tex]175 is a fixed amount added to the mileage reimbursement, regardless of miles driven.
4. Combine to form the total reimbursement equation:
- The total reimbursement, [tex]\( C \)[/tex], is the sum of the mileage reimbursement and the fixed maintenance amount:
[tex]\[
C = 0.45x + 175
\][/tex]
5. Choose the correct option:
- Look at the given options:
- A. [tex]\( C = 45x + 175 \)[/tex]
- B. [tex]\( C = 0.45 + 175 \)[/tex]
- C. [tex]\( C = 0.45x + 175 \)[/tex]
- D. [tex]\( C = 0.45 + 175x \)[/tex]
- The correct equation is:
[tex]\[
C = 0.45x + 175
\][/tex]
- So, the correct choice is option C.
This equation effectively models how the total reimbursement varies with the number of miles driven, incorporating both the variable mileage component and the fixed maintenance component.
