20% of the people are performers for a concert and the rest are spectators. 80% of the spectators are children and there are 1800 less adult spectators than child spectators. How many child spectators must join so that 91% 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		91x1 =  91 u

20% = ²⁰₁₀₀ = ¹₅ 

80% = ⁸⁰₁₀₀ = ⁴₅ 

91% = ⁹¹₁₀₀ = ⁹¹₁₀₀

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 less adult spectators than child spectators at first
= 16 u - 4 u
= 12 u

12 u = 1800

1 u = 1800 ÷ 12 = 150

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

Number of child spectators who must join so that 91% of the people are child spectators
= 91 u - 16 u
= 75 u
= 75 x 150
= 11250

Answer(s): 11250