Answer :
Certainly! Let's break down the problem to understand how we arrive at the correct equation for reimbursement.
We are given that Tim's company reimburses him based on two components:
1. Reimbursement per mile: The company offers [tex]$0.45 per mile.
2. Annual maintenance cost: The company offers a fixed amount of $[/tex]175 for maintenance each year.
To find the total reimbursement, [tex]\( C \)[/tex], we need to consider both the variable component (mileage reimbursement) and the fixed component (annual maintenance):
1. Variable Component: This is the mileage reimbursement. If Tim drives [tex]\( x \)[/tex] miles, the reimbursement part related to mileage would be [tex]\( 0.45 \times x \)[/tex].
2. Fixed Component: This is the annual maintenance reimbursement which is a flat rate of $175, regardless of the number of miles driven.
To create the equation representing the total reimbursement, we simply sum these two components:
[tex]\[
C = 0.45x + 175
\][/tex]
Thus, the correct equation to model the total reimbursement is option B: [tex]\( C = 0.45x + 175 \)[/tex].
This equation incorporates both the mileage reimbursement and the fixed annual maintenance cost, giving the total amount the company offers.
We are given that Tim's company reimburses him based on two components:
1. Reimbursement per mile: The company offers [tex]$0.45 per mile.
2. Annual maintenance cost: The company offers a fixed amount of $[/tex]175 for maintenance each year.
To find the total reimbursement, [tex]\( C \)[/tex], we need to consider both the variable component (mileage reimbursement) and the fixed component (annual maintenance):
1. Variable Component: This is the mileage reimbursement. If Tim drives [tex]\( x \)[/tex] miles, the reimbursement part related to mileage would be [tex]\( 0.45 \times x \)[/tex].
2. Fixed Component: This is the annual maintenance reimbursement which is a flat rate of $175, regardless of the number of miles driven.
To create the equation representing the total reimbursement, we simply sum these two components:
[tex]\[
C = 0.45x + 175
\][/tex]
Thus, the correct equation to model the total reimbursement is option B: [tex]\( C = 0.45x + 175 \)[/tex].
This equation incorporates both the mileage reimbursement and the fixed annual maintenance cost, giving the total amount the company offers.
