A sample of $89$ motels is selected from a large urban area and the price for a night of lodging for a single room was determined for each motel. The mean rate is computed to be $$90$ and the standard deviation is $$13.$ One motel charged $$59$ per night which is the $15$th percentile. Another motel charged $$112$ per night which is the $75$th percentile.

 How many motels charged between $$59$ and $$112?$ Round your answer to the nearest integer.