At $9 per ticket, the teacher can bring "x" students for a total cost of 9x.
However at $6 per ticket, the teacher can bring "x+47" students for the same total cost above. This expression, which is 6(x+47), must then be equal to 9x.
So we have our equation:
9x = 6(x+47)
Solve:
9x = 6x + 282
3x = 282
x = 94
So the teacher can originally bring 94 students to the theater, but since she can bring 47 more students now, she can now bring a grand total of 94 + 47 = 141 students.