Answer :
Sure! To find the equation that models the total reimbursement, we need to understand both components of the reimbursement package:
1. Reimbursement per mile: Donald's company offers [tex]$0.65 per mile. If he drives \( x \) miles, the reimbursement from driving would be \( 0.65 \times x \).
2. Annual maintenance cost: The company also provides a fixed maintenance reimbursement amount of $[/tex]145 per year, regardless of how many miles are driven.
We want to find an equation, [tex]\( C \)[/tex], that gives us the total reimbursement Donald's company offers based on the number of miles [tex]\( x \)[/tex]. This can be expressed as:
[tex]\[ C = \text{(reimbursement per mile)} \times x + \text{(annual maintenance cost)} \][/tex]
Substituting in the given numbers:
[tex]\[ C = 0.65x + 145 \][/tex]
This equation means that for every mile driven, [tex]$0.65 is added up, and a constant $[/tex]145 is added once to account for annual maintenance.
Therefore, the correct equation is found in option B: [tex]\( C = 0.65x + 145 \)[/tex].
1. Reimbursement per mile: Donald's company offers [tex]$0.65 per mile. If he drives \( x \) miles, the reimbursement from driving would be \( 0.65 \times x \).
2. Annual maintenance cost: The company also provides a fixed maintenance reimbursement amount of $[/tex]145 per year, regardless of how many miles are driven.
We want to find an equation, [tex]\( C \)[/tex], that gives us the total reimbursement Donald's company offers based on the number of miles [tex]\( x \)[/tex]. This can be expressed as:
[tex]\[ C = \text{(reimbursement per mile)} \times x + \text{(annual maintenance cost)} \][/tex]
Substituting in the given numbers:
[tex]\[ C = 0.65x + 145 \][/tex]
This equation means that for every mile driven, [tex]$0.65 is added up, and a constant $[/tex]145 is added once to account for annual maintenance.
Therefore, the correct equation is found in option B: [tex]\( C = 0.65x + 145 \)[/tex].
