SOLUTION: In a room with 35 men, 80% of the occupants are women. How many women are in the room?

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Question 174990: In a room with 35 men, 80% of the occupants are women. How many women are in the room?
Found 3 solutions by scott8148, jim_thompson5910, actuary:
Answer by scott8148(6628) About Me  (Show Source):
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if 80% are women, then 20% are men
so there are four times as many women as men
4 * 35 = 140

Answer by jim_thompson5910(35256) About Me  (Show Source):
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Let x=total number of people in room, m=number of men, and w=number of women


Since "80% of the occupants are women", this means that w=0.8x. Solving for "x" and we get w%2F0.8=x ----> x=1.25w


Also, we know that the number of men and women must total the number of people in the room. So this means that m%2Bw=x


m%2Bw=x Start with the given equation.


35%2Bw=1.25w Plug in m=35 (the number of men) and x=1.25w


35=1.25w-w Subtract w from both sides.


35=0.25w Combine like terms.


35%2F0.25=w Divide both sides by 0.25 to isolate "w"


140=w Divide


So the answer is w=140 which means that there are 140 women in the room

Answer by actuary(112) About Me  (Show Source):
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The total number of people in the room expressed as a percent is 100% Since are women, the number of men expressed as a percent is 100% - 80% = 20%
The problem can be solved be setting up the problem as a proportion.
80%/20% = w/35, where w is the number of women in the room. Solve the proportion for w. w = 80/20*35 = 4*35=140. If w = 140 and m =35, the total number of people is 140+35=175.
20%*175=.2*175=35 (OK)
I hope that this helps.