Step 1 :Let's denote the daily fee as \(d\) and the mileage fee as \(m\).
Step 2 :Based on the problem statement, we can write the following equations: \(3d + 300m = 96\) and \(5d + 600m = 171\).
Step 3 :Solving this system of equations will give us the values of \(d\) and \(m\).
Step 4 :The solution to the system of equations gives us the daily fee and the mileage fee. The daily fee is \(d = 21\) and the mileage fee is \(m = 0.11\).
Step 5 :Final Answer: The daily fee is \(\boxed{\$21}\) and the mileage fee is \(\boxed{\$0.11}\). So, the correct answer is C. \$ 21 per day; 11 c per mile.