Question 14
Three towns $X,Y$ and $Z$ lie on a plane with coordinates $(0,0)$, $(200,0)$ and $(0,300)$ respectively. There are 100, 200 and 300 students in town $X,Y$ and $Z$ respectively. A school is to be built on a grid point $(x,y)$, where $x$ and $y$ are both integers, such that the overall distance travelled by all the students is minimized. Find the value of $x+y$.