Answer :
To solve the problem, we need to find the correct equation that models the total amount of reimbursement Donald's company offers based on the given information.
Let's break down the problem:
1. Per Mile Reimbursement: The company reimburses [tex]$0.65 per mile. If Donald drives \( x \) miles, the reimbursement amount for the miles would be \( 0.65 \times x \).
2. Annual Maintenance Cost: The company also offers a fixed yearly maintenance reimbursement of $[/tex]145. This is a constant amount that doesn't depend on the number of miles driven.
3. Total Reimbursement Model: To calculate the total reimbursement (denoted as [tex]\( C \)[/tex]), we need to add the reimbursement for miles to the fixed maintenance cost.
So, the total amount of reimbursement, [tex]\( C \)[/tex], can be expressed as:
[tex]\[ C = 0.65x + 145 \][/tex]
Now let's compare this with the given options:
- Option A: [tex]\( C = 0.65x + 145 \)[/tex] – This equation correctly models the situation.
- Option B: [tex]\( C = 65x + 145 \)[/tex] – This equation incorrectly uses 65 instead of 0.65 for mileage.
- Option C: [tex]\( C = 65 + 145x \)[/tex] – This equation incorrectly places the 145 as a coefficient for [tex]\( x \)[/tex] and uses 65 instead of 0.65.
- Option D: [tex]\( C = 0.65 + 145x \)[/tex] – This equation places 0.65 as a fixed amount rather than a per mile rate.
Therefore, the correct equation that models the total reimbursement is Option A: [tex]\( C = 0.65x + 145 \)[/tex].
Let's break down the problem:
1. Per Mile Reimbursement: The company reimburses [tex]$0.65 per mile. If Donald drives \( x \) miles, the reimbursement amount for the miles would be \( 0.65 \times x \).
2. Annual Maintenance Cost: The company also offers a fixed yearly maintenance reimbursement of $[/tex]145. This is a constant amount that doesn't depend on the number of miles driven.
3. Total Reimbursement Model: To calculate the total reimbursement (denoted as [tex]\( C \)[/tex]), we need to add the reimbursement for miles to the fixed maintenance cost.
So, the total amount of reimbursement, [tex]\( C \)[/tex], can be expressed as:
[tex]\[ C = 0.65x + 145 \][/tex]
Now let's compare this with the given options:
- Option A: [tex]\( C = 0.65x + 145 \)[/tex] – This equation correctly models the situation.
- Option B: [tex]\( C = 65x + 145 \)[/tex] – This equation incorrectly uses 65 instead of 0.65 for mileage.
- Option C: [tex]\( C = 65 + 145x \)[/tex] – This equation incorrectly places the 145 as a coefficient for [tex]\( x \)[/tex] and uses 65 instead of 0.65.
- Option D: [tex]\( C = 0.65 + 145x \)[/tex] – This equation places 0.65 as a fixed amount rather than a per mile rate.
Therefore, the correct equation that models the total reimbursement is Option A: [tex]\( C = 0.65x + 145 \)[/tex].
