Answer :
Sure! Let's break down how to figure out the total reimbursement amount that Tim's company offers based on the number of miles driven.
1. Identify the components of the reimbursement:
- The company offers [tex]$0.45 per mile. This means for every mile driven, Tim receives an additional $[/tex]0.45.
- Additionally, the company provides a fixed amount of [tex]$175 per year for maintenance, regardless of the number of miles driven.
2. Define variables and equation:
- Let \( x \) represent the number of miles driven.
- The total reimbursement, \( C \), will be the sum of two parts:
- The mileage reimbursement: \( 0.45 \times x \)
- The fixed maintenance amount: $[/tex]175
3. Combine the components into an equation:
- The total amount of reimbursement, [tex]\( C \)[/tex], is the sum of the mileage reimbursement and the maintenance fee, which gives us:
[tex]\[
C = 0.45x + 175
\][/tex]
This equation models how Tim's company calculates the total reimbursement based on the miles driven. Comparing with the choices given:
- A. [tex]\( C = 0.45 + 175 \)[/tex]: Incorrect, because it doesn't account for mileage.
- B. [tex]\( C = 0.45 + 175x \)[/tex]: Incorrect, the terms involving mileage and maintenance are not correctly placed.
- C. [tex]\( C = 45x + 175 \)[/tex]: Incorrect, the rate per mile should be [tex]$0.45, not $[/tex]45.
- D. [tex]\( C = 0.45x + 175 \)[/tex]: This is the correct equation.
This equation matches the components necessary for calculating the reimbursement. So, the total reimbursement amount [tex]\( C \)[/tex] given by Tim's company is modeled by this equation. Option D is the correct answer.
1. Identify the components of the reimbursement:
- The company offers [tex]$0.45 per mile. This means for every mile driven, Tim receives an additional $[/tex]0.45.
- Additionally, the company provides a fixed amount of [tex]$175 per year for maintenance, regardless of the number of miles driven.
2. Define variables and equation:
- Let \( x \) represent the number of miles driven.
- The total reimbursement, \( C \), will be the sum of two parts:
- The mileage reimbursement: \( 0.45 \times x \)
- The fixed maintenance amount: $[/tex]175
3. Combine the components into an equation:
- The total amount of reimbursement, [tex]\( C \)[/tex], is the sum of the mileage reimbursement and the maintenance fee, which gives us:
[tex]\[
C = 0.45x + 175
\][/tex]
This equation models how Tim's company calculates the total reimbursement based on the miles driven. Comparing with the choices given:
- A. [tex]\( C = 0.45 + 175 \)[/tex]: Incorrect, because it doesn't account for mileage.
- B. [tex]\( C = 0.45 + 175x \)[/tex]: Incorrect, the terms involving mileage and maintenance are not correctly placed.
- C. [tex]\( C = 45x + 175 \)[/tex]: Incorrect, the rate per mile should be [tex]$0.45, not $[/tex]45.
- D. [tex]\( C = 0.45x + 175 \)[/tex]: This is the correct equation.
This equation matches the components necessary for calculating the reimbursement. So, the total reimbursement amount [tex]\( C \)[/tex] given by Tim's company is modeled by this equation. Option D is the correct answer.
