40% of the people are performers for a concert and the rest are spectators. 70% of the spectators are adults and there are 1800 less child spectators than adult spectators. How many adult spectators must join so that 71% of the people are adult spectators?

	Performers	Spectators
	2x10	3x10
		Children	Adults
		3x3	7x3
Before	20 u	9 u	21 u
Change			+ ?
After	29x1 = 29 u		71x1 =  71 u

40% = ⁴⁰₁₀₀ = ²₅ 

70% = ⁷⁰₁₀₀ = ⁷₁₀ 

71% = ⁷¹₁₀₀ = ⁷¹₁₀₀

The total number of spectators at first is repeated.  Make the total number of spectators the same.  LCM of 3 and 10 is 30.

Number of less child spectators than adult spectators at first
= 21 u - 9 u
= 12 u

12 u = 1800

1 u = 1800 ÷ 12 = 150

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

Number of adult spectators who must join so that 71% of the people are adult spectators
= 71 u - 21 u
= 50 u
= 50 x 150
= 7500

Answer(s): 7500