Question

keith will rent a car for the weekend. he can choose one of two plans. the first plan has an initial fee of $44 and costs an additional $0.12 per mile driven. the second plan has an initial fee of $57 and costs an additional $0.08 per mile driven.
for what amount of driving do the two plans cost the same?
125 miles
what is the cost when the two plans cost the same?
$

Explanation:

Step1: Define variables and cost functions

Let \( m \) be the number of miles driven. The cost of the first plan \( C_1 \) is \( C_1 = 44 + 0.12m \). The cost of the second plan \( C_2 \) is \( C_2 = 57 + 0.08m \).

Step2: Set costs equal to find miles

Set \( C_1 = C_2 \):
\( 44 + 0.12m = 57 + 0.08m \)
Subtract \( 0.08m \) from both sides:
\( 44 + 0.04m = 57 \)
Subtract 44 from both sides:
\( 0.04m = 13 \)
Divide both sides by 0.04:
\( m=\frac{13}{0.04}=325 \) (miles, which matches the given value)

Step3: Calculate the cost

Use either cost function. Let's use \( C_1 \):
\( C_1 = 44 + 0.12\times325 \)
\( C_1 = 44 + 39 \)
\( C_1 = 83 \)

Answer:

\$83