Mrs. Scott is preparing for the upcoming school musical. She spends $350 on costumes and props for e the students and $322 on the elaborate set. She plans I on selling student tickets for $7, adult tickets for $9, and , teacher tickets for $5. If she hopes to make a profit of $208 and needs to sell 5 times as many adult tickets as 5 teacher tickets and 20 less student tickets than adult tickets, how many of each type of ticket does she need to sell to reach her goal?