SOLUTION: 1/2 kids have left party 18 kids are standing around 1/3 are dancing how many kids were originally at party

Question 6924: 1/2 kids have left party
18 kids are standing around
1/3 are dancing
how many kids were originally at party
Found 2 solutions by Earlsdon, glabow:
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Let x be the number of kids originally at the party.
Then:
(1/2)x + 18 + (1/3)x = x Simplify and solve for x.
(1/2)x + (1/3)x + 18 = x Add the fractions of x, common denominator is 6.
(3/6)x + (2/6)x + 18 = x
(5/6)x + 18 = x Subtract (5/6)x from both sides.
18 = x - (5/6)x
18 = (1/6)x Multiply both sides by 6.
x = 108 The number of kids originally at the party.
Check:
(1/2)(108) + 18 + (1/3)(108) = 54 + 18 + 36 = 108

Answer by glabow(165) (Show Source): You can put this solution on YOUR website!
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.
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