¹₈ of the people at a stadium were girls. 70% of the remaining people were boys and the rest were adults. The total number of girls and adults is 162 less than the number of boys. After some boys entered the stadium, 75% of the people that remained were boys. How many boys entered the stadium?

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

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

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

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

The total number of girls and adults is 162 less than the number of boys.

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

18 u = 162

1 u = 162 ÷ 18 = 9

Number of boys who entered the stadium
= 93 u - 49 u
= 44 u
= 44 x 9
= 396

Answer(s): 396