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assuming that temperature is constant and that we're talking about regular party balloons (a "regular" 2-gram party balloon can hold ~ 16 grams of gas), you would need 6,156 baloons to hold your weight in equilibrium. you would need an amount greater than this to actually lift you (the more extra balloons, the faster the lift), and this is not accounting for the weight of the string.
extrapolated from: http://Malaysia.answers.Yahoo.com/question/index?qid=1005123102737
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