Source: 2017 Canadian Open Math Challenge, Problem B1 Andrew and Beatrice practice their free throws in basketball. One day, they attempted a total of $105$ free throws between them, with each person taking at least one free throw. If Andrew made exactly $1/3$ of his free throw attempts and Beatrice made exactly $3/5$ of her free throw attempts, what is the highest number of successful free throws they could have made between them?