our dorm bathroom is tiled using white hexagonal tiles arranged in a honeycomb pattern (see the figure). One weekend, you and your roommates decide to replace all the white tiles with purple and gold tiles in honor of your school colors, with some green tiles thrown in as accents. (One of your roommates is from New Orleans.) You need a total of 7200 tiles. You want three times as many gold tiles as green tiles, and 1200 more purple tiles than twice the number of green tiles. How many tiles of each color do you need?