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

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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

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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 . Solving for "x" and we get ---->


Also, we know that the number of men and women must total the number of people in the room. So this means that


Start with the given equation.


Plug in (the number of men) and


Subtract w from both sides.


Combine like terms.


Divide both sides by 0.25 to isolate "w"


Divide


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

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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.