30% of the people are performers for a concert and the rest are spectators. 60% of the spectators are adults and there are 1050 less child spectators than adult spectators. How many adult spectators must join so that 71% of the people are adult spectators?

	Performers	Spectators
	3x5	7x5
		Children	Adults
		2x7	3x7
Before	15 u	14 u	21 u
Change			+ ?
After	29x1 = 29 u		71x1 =  71 u

30% = ³⁰₁₀₀ = ³₁₀ 

60% = ⁶⁰₁₀₀ = ³₅ 

71% = ⁷¹₁₀₀ = ⁷¹₁₀₀

The total number of spectators at first is repeated.  Make the total number of spectators the same.  LCM of 7 and 5 is 35.

Number of less child spectators than adult spectators at first
= 21 u - 14 u
= 7 u

7 u = 1050

1 u = 1050 ÷ 7 = 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