Lucy is planning a birthday party and wants to invite her friends. She is 25 years old and plans to invite a number of friends equal to her age. Each friend will receive a party favor bag, and each bag costs $2. Lucy also wants to buy a birthday cake that costs $30. If she has a budget of $100 for the party, how much money will she have left after buying the party favor bags and the cake? Let's think step by step and output the final answer within \boxed{}.
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