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Answered 2010-04-07 21:32:21

After half the people left, there were 54 in the room, of whom 18 danced. There were originally 108 people in the room.

No, in a word problem it is very important to READ CAREFULLY! Of course, some punctuation in the problem would have helped! But there were 18 people NOT dancing. So to find the number of people remaining in the room:

2/3 of the remaining people = 18, so 1/3 of the remaining people = 9, (1/3 is half of 2/3)

So then 2/3 + 1/3 = total number of people remaining in the room: 18 + 9 = 27, which is half the original number.

So 27 + 27 = 54, which is the number of people originally in the room.

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