jmc

Let the number of girls at HMS be $g$ and the number of boys be $b$. Thus, the total number of students implies $g+b=1200$ and the attendance figures imply $\frac{2}{3}g+\frac{1}{2}b=730$. Multiplying the first equation by 3 and subtracting that from the second equation multiplied by 6, we get $g=780$. And, the number of girls who attended the picnic is $\frac{2}{3}\cdot 780=\boxed{520}$.