¹₈ of the people at a concert hall were boys. 70% of the remaining people were girls and the rest were adults. The total number of boys and adults is 342 less than the number of girls. After some girls entered the concert hall, 75% of the people that remained were girls. How many girls entered the concert hall?

Boys	Adults	Girls	Total
1x10	7x10		8x10
	3x7	7x7
10	21	49	80

	Boys and adults	Girls
Before	31x1 = 31 u	49x1 = 49 u
Change		+ 44 u
After	1x31 = 31 u	3x31 = 93 u

70% = ⁷⁰₁₀₀ = ⁷₁₀
Adults : Girls = 3 : 7

The total number of adults and girls at first is repeated.  Make the total number of adults at first the same. LCM of 7 and 10 is 70.

75% = ⁷⁵₁₀₀ = ³₄

When some girls entered, the total number of boys and adults remains unchanged. Make the total number of boys and adults the same. LCM of 31 and 1 is 31.

The total number of boys and adults is 342 less than the number of girls.

Number of less boys and adults than the number of girls at first
= 49 u - 31 u
= 18 u

18 u = 342

1 u = 342 ÷ 18 = 19

Number of girls who entered the concert hall
= 93 u - 49 u
= 44 u
= 44 x 19
= 836

Answer(s): 836