A bag initially contains green marbles and orange marbles only, with more orange than green. Green marbles are added to the bag until only $\frac{1}{4}$ of the marbles in the bag are orange. Then purple marbles are added to the bag until only $\frac{1}{6}$ of the marbles in the bag are orange. Finally, the number of orange marbles in the bag is tripled. What fraction of the marbles now in the bag are orange?