A factory produces three types of widgets: A, B, and C. Each type of widget requires a different amount of time to manufacture. Widget A takes 2 hours to produce, Widget B takes 3 hours, and Widget C takes 4 hours. If the factory operates for 24 hours a day and produces a total of 10 widgets, how many of each type of widget were produced if the total production time for all widgets is 30 hours? Let's think step by step and output the final answer within \boxed{}.
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