Answer :
Sure, let's solve the problem step-by-step.
We are given that Tim’s company reimburses \[tex]$0.45 per mile and provides an additional \$[/tex]175 per year for maintenance. We need to find an equation that models [tex]\( C \)[/tex], the total amount of reimbursement, if [tex]\( x \)[/tex] represents the number of miles driven in a year.
Step-by-Step Solution:
1. Identify the variables and constants:
- Let [tex]\( x \)[/tex] be the number of miles driven in a year.
- The reimbursement rate per mile is \[tex]$0.45.
- The fixed annual maintenance amount is \$[/tex]175.
2. Construct the equation for the total reimbursement [tex]\( C \)[/tex]:
- The amount reimbursed per mile driven is calculated by multiplying the number of miles ([tex]\( x \)[/tex]) by the reimbursement rate per mile (\[tex]$0.45). This can be expressed as \( 0.45x \).
- The total reimbursement also includes the fixed annual maintenance amount, which is \$[/tex]175.
3. Combine these components to form the total reimbursement equation:
- The total reimbursement [tex]\( C \)[/tex] is the sum of the reimbursement for the miles driven and the fixed annual maintenance amount.
- Therefore, the equation can be written as:
[tex]\[
C = 0.45x + 175
\][/tex]
4. Match the equation with the given choices:
- Choice A: [tex]\( C = 0.45x + 175 \)[/tex]
- Choice B: [tex]\( C = 0.45 + 175x \)[/tex]
- Choice C: [tex]\( C = 45x + 175 \)[/tex]
- Choice D: [tex]\( C = 0.45 + 175 \)[/tex]
5. Select the correct answer:
- The correct equation that models the total amount of reimbursement [tex]\( C \)[/tex] is given by choice A:
[tex]\[
C = 0.45x + 175
\][/tex]
So, the correct answer is A. [tex]\( C = 0.45x + 175 \)[/tex].
We are given that Tim’s company reimburses \[tex]$0.45 per mile and provides an additional \$[/tex]175 per year for maintenance. We need to find an equation that models [tex]\( C \)[/tex], the total amount of reimbursement, if [tex]\( x \)[/tex] represents the number of miles driven in a year.
Step-by-Step Solution:
1. Identify the variables and constants:
- Let [tex]\( x \)[/tex] be the number of miles driven in a year.
- The reimbursement rate per mile is \[tex]$0.45.
- The fixed annual maintenance amount is \$[/tex]175.
2. Construct the equation for the total reimbursement [tex]\( C \)[/tex]:
- The amount reimbursed per mile driven is calculated by multiplying the number of miles ([tex]\( x \)[/tex]) by the reimbursement rate per mile (\[tex]$0.45). This can be expressed as \( 0.45x \).
- The total reimbursement also includes the fixed annual maintenance amount, which is \$[/tex]175.
3. Combine these components to form the total reimbursement equation:
- The total reimbursement [tex]\( C \)[/tex] is the sum of the reimbursement for the miles driven and the fixed annual maintenance amount.
- Therefore, the equation can be written as:
[tex]\[
C = 0.45x + 175
\][/tex]
4. Match the equation with the given choices:
- Choice A: [tex]\( C = 0.45x + 175 \)[/tex]
- Choice B: [tex]\( C = 0.45 + 175x \)[/tex]
- Choice C: [tex]\( C = 45x + 175 \)[/tex]
- Choice D: [tex]\( C = 0.45 + 175 \)[/tex]
5. Select the correct answer:
- The correct equation that models the total amount of reimbursement [tex]\( C \)[/tex] is given by choice A:
[tex]\[
C = 0.45x + 175
\][/tex]
So, the correct answer is A. [tex]\( C = 0.45x + 175 \)[/tex].
