A hotel rents rooms to customers by the night. The hotel determines that if it sets the price of the room to be $150 per​ night, 140 rooms will be rented. In order to rent 190 rooms, it must lower the price to $100 per night. What price must it set in order to maximize​ revenue?   The price would be $            per night. ​(Round answer to two decimal​ places.)

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