A hotel that has $200$ rooms charges a rate of $$200$ per night Monday through Thursday. During this period of peak demand, the hotel operates at $100$ percent capacity. On weekends $($Friday through Sunday$),$ the hotel discounts half of its rooms at a rate of $$100$ per night while the remaining rooms are still priced at $$200$ per night. Calculate the hotel's yield for a Saturday night, if it fills $50$ percent of the $$200$ rooms and sells all of the $$100$ rooms. Round to the nearest percent.