Let $x$ be the number of students who only attended music class, $y$ be the number of students who only attended art class, and $z$ be the number of students who attended both music and art classes. We are given the following information:

Total number of students = 400

$x + y + z = 400$

Percentage of students who attended music class = 75%

Number of students who attended music class = $0.75 \times 400 = 300$

$x + z = 300$

Percentage of students who attended art class = 50%

Number of students who attended art class = $0.50 \times 400 = 200$

$y + z = 200$

We have three equations:

1. $x + y + z = 400$
2. $x + z = 300$
3. $y + z = 200$

From equation (1) and (2), we have: $(x + z) + y = 400$ $300 + y = 400$ $y = 100$

From equation (3), we have: $y + z = 200$ $100 + z = 200$ $z = 100$

From equation (2), we have: $x + z = 300$ $x + 100 = 300$ $x = 200$

The number of students who attended both music and art classes is $z = 100$.

Therefore, the number of students who attended both classes is 100. Final Answer: The final answer is $\boxed{100}$