10% of the people are performers for a concert and the rest are spectators. 80% of the spectators are adults and there are 1080 less child spectators than adult spectators. How many adult spectators must join so that 86% of the people are adult spectators?

	Performers	Spectators
	1x5	9x5
		Children	Adults
		1x9	4x9
Before	5 u	9 u	36 u
Change			+ ?
After	7x2 = 14 u		43x2 =  86 u

10% = ¹⁰₁₀₀ = ¹₁₀ 

80% = ⁸⁰₁₀₀ = ⁴₅ 

86% = ⁸⁶₁₀₀ = ⁴³₅₀

The total number of spectators at first is repeated.  Make the total number of spectators the same.  LCM of 9 and 5 is 45.

Number of less child spectators than adult spectators at first
= 36 u - 9 u
= 27 u

27 u = 1080

1 u = 1080 ÷ 27 = 40

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

Number of adult spectators who must join so that 86% of the people are adult spectators
= 86 u - 36 u
= 50 u
= 50 x 40
= 2000

Answer(s): 2000