3. Villages $A, B$ and $C$ are located at the vertices of an equilateral triangle. In village $A$, there are 100 schoolchildren, in village $B-200$, in village $C-300$. Where should a school be built so that the total distance traveled by all schoolchildren is as small as possible?
76.3. Answer. In village $C$. If it is built at any other point $X$, then when it is moved to $C$, the total distance traveled by the schoolchildren will change by $300|C X|-100(|A X|-$ $-|A C|)-200(|B X|-|B A|)$, i.e., it will obviously decrease, since $|A X|-|A C| \leqslant|C X|,|B X|-|B C| \leqslant|C X|$.