To determine which equation correctly models the total amount of reimbursement [tex]\( C \)[/tex] that Dean's company offers, we need to analyze the components of the reimbursement package:
1. Cost per mile: Dean’s company offers [tex]\( \$0.59 \)[/tex] per mile. This amount will vary based on the number of miles [tex]\( x \)[/tex] driven.
2. Annual maintenance: Dean’s company offers a fixed amount of [tex]\( \$275 \)[/tex] per year for maintenance, irrespective of the number of miles driven.
To find the total reimbursement [tex]\( C \)[/tex], we combine these two components:
1. The variable component is [tex]\( \$0.59 \)[/tex] per mile. For [tex]\( x \)[/tex] miles, this component is [tex]\( 0.59x \)[/tex].
2. The fixed component is the [tex]\( \$275 \)[/tex] annual maintenance.
Hence, the equation can be modeled as:
[tex]\[ C = 0.59x + 275 \][/tex]
Now let's compare this to the given options:
A. [tex]\( C = 59x + 275 \)[/tex]
- This option incorrectly states the cost per mile as [tex]\( \$59 \)[/tex], which is much higher than the correct rate of [tex]\( \$0.59 \)[/tex].
B. [tex]\( C = 0.59x + 275 \)[/tex]
- This option correctly represents the reimbursement amount, combining [tex]\( \$0.59 \)[/tex] per mile with the fixed [tex]\( \$275 \)[/tex] for annual maintenance.
C. [tex]\( C = 0.59 + 275x \)[/tex]
- This option incorrectly reverses the coefficients, placing [tex]\( 0.59 \)[/tex] as a fixed component and allocating [tex]\( 275x \)[/tex], which doesn't match the given reimbursement package structure.
D. [tex]\( C = 59x + 275 \)[/tex]
- This option is identical to option A and is incorrect for the same reason.
Therefore, the correct equation that models the total amount of reimbursement the company offers is:
[tex]\[ \boxed{C = 0.59x + 275} \][/tex]
