Q. At a party each man danced with exactly four women and each women danced with exactly three men . Nine women attented the party .How many women attented the party?

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Solution

Since there are 9 men and each man dances with 4 women (presumably this means each man dances exactly 4 times), there are exactly 36 dance pairs.

Let x be the number of women.

Since each woman dances with 3 men (presumably this means each woman dances exactly 3 times), there are exactly 3x dance pairs.

Thus, 3x=36, so x=12
so 12 women attended the party.

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