Sarah is planning a birthday party for her daughter. She has a budget of $200. She spends $50 on decorations, $70 on food, and $30 on party favors. She also needs to buy a cake that costs $4 per slice, and she plans to buy 12 slices. After purchasing everything, how much money does she have left in her budget? Let's think step by step and output the final answer within \boxed{}.
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