A lemonade stand sells lemonade at a rate of $3 per cup. The stand operates for 5 hours a day. During the first 2 hours, they sell 10 cups of lemonade each hour. In the next 3 hours, they sell 15 cups per hour. If the stand incurs a fixed cost of $30 per day for supplies and operation, how much profit does the lemonade stand make in a day? Let's think step by step and output the final answer within \boxed{}.
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