Mr$.$Matsura is a famous motivational speaker. He travels across the country by jet and gives an average of nine presentations a week. He gives his speeches in auditoriums that are always full and hold an average of $2500$ people each. He charges $$20$ per person at each of these speeches. His average expenses for each presentation, including renting the auditorium, are about $$13,000.$ The cost of meals, motels, jet travel, and support personnel total $$75,000$ per week. How many weeks will Mr$.$Matsura need to travel if he wants to earn $$516,000$ per year?