To solve this problem, we can set up an equation with two variables. Let:
- \( x \): number of students (in this case, 25)
- \( y \): total cost of the trip
The total cost includes a flat rate plus the cost per ticket. The equation for the total cost can be expressed as:
\[ y = 50 + 15x \]
Substituting \( x = 25 \) (the number of students):
\[ y = 50 + 15(25) \] \[ y = 50 + 375 \] \[ y = 425 \]
Thus, the total cost for the school to take a class of 25 students to see The Nutcracker would be \( \text{$425.00} \).
The correct answer is $425.00.