25% of the people are performers for a concert and the rest are spectators. 60% of the spectators are children and there are 150 less adult spectators than child spectators. How many child spectators must join so that 78% of the people are child spectators?

	Performers	Spectators
	1x5	3x5
		Adults	Children
		2x3	3x3
Before	5 u	6 u	9 u
Change			+ ?
After	11x1 = 11 u		39x1 =  39 u

25% = ²⁵₁₀₀ = ¹₄ 

60% = ⁶⁰₁₀₀ = ³₅ 

78% = ⁷⁸₁₀₀ = ³⁹₅₀

The total number of spectators at first is repeated.  Make the total number of spectators the same.  LCM of 3 and 5 is 15.

Number of less adult spectators than child spectators at first
= 9 u - 6 u
= 3 u

3 u = 150

1 u = 150 ÷ 3 = 50

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

Number of child spectators who must join so that 78% of the people are child spectators
= 39 u - 9 u
= 30 u
= 30 x 50
= 1500

Answer(s): 1500