A high school has 300 freshmen and 250 sophomores. The average age of the freshmen is 14.5 years, and the average age of the sophomores is 15.2 years. If a group of 50 students, consisting of 20 freshmen and 30 sophomores, transfers to another school, what is the new average age of the remaining students at the high school? Round your answer to the nearest tenth of a year.