Let x variable represent the amount of younger students.

Let y varialbe represent the amount of older students.

Then, x+y <= 100

Each x costs $3 thus in total 3x dollars.

Each y costs $6 thus in total 6y dollars.

The net total is, 3x+6y.

Then, 3x+6y<=400

This yields two inequalities,

x+y<=100

3x+6y<=400

But there are two more, x>=0 and y>=0

These are natural inequalities.

Since you cannot have a negative amount of students going.

So we really have,

x+y<=100

3x+6y<=400

x>=0 and y>=0