The workers in a factory produce widgets and whoosits. For each product, production time is constant and identical for all workers, but not necessarily equal for the two products. In one hour, $$100$$ workers can produce $$300$$ widgets and $$200$$ whoosits. In two hours, $$60$$ workers can produce $$240$$ widgets and $$300$$ whoosits. In three hours, $$50$$ workers can produce $$150$$ widgets and $$m$$ whoosits. Find $$m$$.

(第二十五届AIME2 2007 第4题)