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Andy was on his way to a marble tournament when he met Bob. Andy's bag of marbles was heavy, so he gave Bob 1/2 of his marbles plus 2. Then he met Alex and gave him 1/4 of his remaining marbles plus 5. Just before arriving at the tournament, he met Emily and gave her 1/2 of the marbles he had left. When he got to the tournament, he had 2 marbles left. HOW MANY MARBLES DID HE START WITH?

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