A room contains 96 people. A man leaves and is replaced ny a women, leaving three times as many women as men in the room. How many men and women were there originally ?

Question

anonymous · Answer

W:M=3:1=3*(96/4):(96/4)=72:24
Women: 71, Men: 25

directrix · Answer

Let M = the original number of Men 
Let W = the original number of Women
----------
M + W = 96 *
3( M - 1) = (W + 1)
3M - 3 = W + 1
3M - 4 = W **
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M + W = 96 *  -- > W = 96 - M
3M - 4 = W **
Substitute 96 - M for W
3M - 4 =  96 - M
4M = 100
M = 25----->Orignal Number of Men
W = 96 - M = 96 - 25 = 71 --> Original Number of Women