Answer :
Sure! Let's break down the problem step-by-step to understand which equation models the total amount of reimbursement that Donald's company offers.
1. Understand the Reimbursement Structure:
- The company reimburses [tex]$0.65 per mile driven.
- Additionally, there is a fixed reimbursement of $[/tex]145 per year for maintenance.
2. Define the Variables:
- Let [tex]\( x \)[/tex] represent the number of miles driven by Donald.
- Let [tex]\( C \)[/tex] represent the total reimbursement amount.
3. Construct the Equation:
- The reimbursement for the miles driven is calculated by multiplying the cost per mile by the number of miles: [tex]\( 0.65 \times x \)[/tex].
- The total fixed annual maintenance reimbursement is [tex]\( 145 \)[/tex].
4. Combine These Components to Formulate the Total Reimbursement:
- The total reimbursement [tex]\( C \)[/tex] is the sum of the mileage reimbursement and the fixed maintenance amount.
- Therefore, the equation is:
[tex]\[
C = 0.65x + 145
\][/tex]
5. Match With Given Options:
- Let's compare this equation to the provided options:
- Option A: [tex]\( C = 0.65 + 145x \)[/tex]
- Option B: [tex]\( C = 0.65x + 145 \)[/tex]
- Option C: [tex]\( C = 65x + 145 \)[/tex]
- Option D: [tex]\( C = 65 + 145x \)[/tex]
6. Conclusion:
- The correct equation that models the total amount of reimbursement is Option B: [tex]\( C = 0.65x + 145 \)[/tex].
This equation correctly represents the combination of mileage reimbursement and the annual maintenance cost.
1. Understand the Reimbursement Structure:
- The company reimburses [tex]$0.65 per mile driven.
- Additionally, there is a fixed reimbursement of $[/tex]145 per year for maintenance.
2. Define the Variables:
- Let [tex]\( x \)[/tex] represent the number of miles driven by Donald.
- Let [tex]\( C \)[/tex] represent the total reimbursement amount.
3. Construct the Equation:
- The reimbursement for the miles driven is calculated by multiplying the cost per mile by the number of miles: [tex]\( 0.65 \times x \)[/tex].
- The total fixed annual maintenance reimbursement is [tex]\( 145 \)[/tex].
4. Combine These Components to Formulate the Total Reimbursement:
- The total reimbursement [tex]\( C \)[/tex] is the sum of the mileage reimbursement and the fixed maintenance amount.
- Therefore, the equation is:
[tex]\[
C = 0.65x + 145
\][/tex]
5. Match With Given Options:
- Let's compare this equation to the provided options:
- Option A: [tex]\( C = 0.65 + 145x \)[/tex]
- Option B: [tex]\( C = 0.65x + 145 \)[/tex]
- Option C: [tex]\( C = 65x + 145 \)[/tex]
- Option D: [tex]\( C = 65 + 145x \)[/tex]
6. Conclusion:
- The correct equation that models the total amount of reimbursement is Option B: [tex]\( C = 0.65x + 145 \)[/tex].
This equation correctly represents the combination of mileage reimbursement and the annual maintenance cost.
