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If the ratio of men to women is 3:1 and there are 32 female performers, we can determine the number of men by first recognizing that for every 3 men, there is 1 woman. Therefore, the number of women (32) represents the 1 part of the ratio. This means there are 3 parts for the men, so the number of men is 32 multiplied by 3, resulting in 96 men in the dance recital.

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