MathDB

There are three bags of marbles. Bag two has twice as many marbles as bag one. Bag three has three times as many marbles as bag one. Half the marbles in bag one, one third the marbles in bag two, and one fourth the marbles in bag three are green. If all three bags of marbles are dumped into a single pile,

\frac{m}{n}

of the marbles in the pile would be green where

m

and

n

are relatively prime positive integers. Find

m + n.

Problem Statement