20% of the people are performers for a concert and the rest are spectators. 60% of the spectators are children and there are 560 less adult spectators than child spectators. How many child spectators must join so that 74% of the people are child spectators?

	Performers	Spectators
	1x5	4x5
		Adults	Children
		2x4	3x4
Before	5 u	8 u	12 u
Change			+ ?
After	13x1 = 13 u		37x1 =  37 u

20% = ²⁰₁₀₀ = ¹₅ 

60% = ⁶⁰₁₀₀ = ³₅ 

74% = ⁷⁴₁₀₀ = ³⁷₅₀

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
= 12 u - 8 u
= 4 u

4 u = 560

1 u = 560 ÷ 4 = 140

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

Number of child spectators who must join so that 74% of the people are child spectators
= 37 u - 12 u
= 25 u
= 25 x 140
= 3500

Answer(s): 3500