30% of the people are performers for a concert and the rest are spectators. 60% of the spectators are children and there are 490 less parent spectators than child spectators. How many child spectators must join so that 71% of the people are child spectators?

	Performers	Spectators
	3x5	7x5
		Parents	Children
		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 parent spectators than child spectators at first
= 21 u - 14 u
= 7 u

7 u = 490

1 u = 490 ÷ 7 = 70

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

Number of child spectators who must join so that 71% of the people are child spectators
= 71 u - 21 u
= 50 u
= 50 x 70
= 3500

Answer(s): 3500