Question 6924
I get a different answer.
Let x be the number of kids originally at the party.
Then after half leave, x/2 remain. 
Of these, 1/3 are dancing. That is, x/6 are dancing.
18 are just standing around.
So, x/6 + 18 = x/2
Solving,
x/6 - x/2 = -18
x/6 - 3x/6 = -18
x - 3x = -108
-2x = -108
x= 54
There were orginally 54 kids. Half left, leaving 27. Of these, 1/3 are dancing = 9. The remaining 18 are standing around.