Sophia is planning a road trip and wants to ensure she has enough fuel for the journey. Her car's fuel tank holds 15 gallons, and her car gets 30 miles per gallon. She plans to travel a total of 450 miles. Sophia knows that gas stations are sparse along her route, so she wants to calculate how many full tanks of gas she will need and how much extra fuel she will require to complete her trip. Additionally, if gas costs $3.50 per gallon, how much will she spend on fuel for the entire trip? Let's think step by step and output the final answer within \boxed{}.
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