20% of the people are performers for a concert and the rest are spectators. 80% of the spectators are children and there are 600 more child spectators than adult spectators. How many child spectators must leave so that 55% of the people are child spectators?

	Performers	Spectators
	1x5	4x5
		Adults	Children
		1x4	4x4
Before	5 u	4 u	16 u
Change			- ?
After	9x1 = 9 u		11x1 =  11 u

20% = ²⁰₁₀₀ = ¹₅ 

80% = ⁸⁰₁₀₀ = ⁴₅ 

55% = ⁵⁵₁₀₀ = ¹¹₂₀

The total number of spectators at first is repeated.  Make the total number of spectators the same.  LCM of 4 and 5 is 20.

Number of more child spectators than adult spectators at first
= 16 u - 4 u
= 12 u

12 u = 600

1 u = 600 ÷ 12 = 50

If some child spectators leave, the total number of adult spectators and performers remains unchanged.  

Number of child spectators who must leave so that 55% of the people are child spectators
= 16 u - 11 u
= 5 u
= 5 x 50
= 250

Answer(s): 250