20% of the people are performers for a concert and the rest are spectators. 80% of the spectators are parents and there are 360 more parent spectators than child spectators. How many parent spectators must leave so that 55% of the people are parent spectators?

	Performers	Spectators
	1x5	4x5
		Children	Parents
		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 parent spectators than child spectators at first
= 16 u - 4 u
= 12 u

12 u = 360

1 u = 360 ÷ 12 = 30

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

Number of parent spectators who must leave so that 55% of the people are parent spectators
= 16 u - 11 u
= 5 u
= 5 x 30
= 150

Answer(s): 150