A performance at the Bingham Performing Arts Center was attended by 100 people. The audience consisted of​ adults, students, and children. The ticket prices were ​$9 each for​ adults, ​$3 each for​ students, and 50 cents each for children. The total amount of money taken in was ​$100. How many​ adults, students, and children were in​ attendance? Does there seem to be some information​ missing? Do some careful reasoning.