What is your thought process when you begin to translate a problem like this into Algebra? Is it just a matter of practicing problems in order to get better at it? Here it is:

A room contains 160 people, 15 percent of whom are women. A group of people, 30 percent of whom are women, leaves the room. Of the people remaining in the room, 10 percent are women. How many people left the room?

A. 10

B. 20

C. 40

D. 60

E. 80

I know the official answer explanation and it makes sense when I read it. But, I am trying to get better at seeing how to quickly setup a problem like this in order to solve it in less than 2 minutes.

.15*160 = 24, the number of women in the room.

I guess the key is to set x = group of people that left the room.

Then, .3x = the number of women in this group.

Next, the people remaining in the room is (160-x), .1 of which are women.

So, 24-.3x = .1(160-x)

Maybe what I should do is take one sentence at a time in the question stem and translate into Algebra, like I did above. Then, see how I can piece it together. Sort of like I did above.

Like I said, I am a little fuzzy about how to think about this. I would appreciate any help. Thanks!

Thanks!

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