Joan and Dick spent 35 nights touring four cities on the East Coast--Boston, New York, Philadelphia, and Washington. They paid $121, $192, $82, and $103 per night for lodging in each city, respectively, and their total hotel bill came to $4853. The number of days they spent in New York was the same as the total number of days they spent in Boston and Washington, and the couple spent 3 times as many days in New York as they did in Philadelphia. How many days did Joan and Dick stay in each city? (system of linear equations)