40% of the people are performers for a concert and the rest are spectators. 80% of the spectators are parents and there are 900 less child spectators than parent spectators. How many parent spectators must join so that 87% of the people are parent spectators?

	Performers	Spectators
	2x5	3x5
		Children	Parents
		1x3	4x3
Before	10 u	3 u	12 u
Change			+ ?
After	13x1 = 13 u		87x1 =  87 u

40% = ⁴⁰₁₀₀ = ²₅ 

80% = ⁸⁰₁₀₀ = ⁴₅ 

87% = ⁸⁷₁₀₀ = ⁸⁷₁₀₀

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 child spectators than parent spectators at first
= 12 u - 3 u
= 9 u

9 u = 900

1 u = 900 ÷ 9 = 100

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

Number of parent spectators who must join so that 87% of the people are parent spectators
= 87 u - 12 u
= 75 u
= 75 x 100
= 7500

Answer(s): 7500