¹₁₀ of the guests at a stadium were girls. 80% of the remaining guests were boys and the rest were adults. The total number of girls and adults is 132 less than the number of boys. After some boys entered the stadium, 75% of the guests that remained were boys. How many boys entered the stadium?

Girls	Adults	Boys	Total
1x5	9x5		10x5
	1x9	4x9
5	9	36	50

	Girls and adults	Boys
Before	14x1 = 14 u	36x1 = 36 u
Change		+ 6 u
After	1x14 = 14 u	3x14 = 42 u

80% = ⁸⁰₁₀₀ = ⁴₅
Adults : Boys = 1 : 4

The total number of adults and boys at first is repeated.  Make the total number of adults at first the same. LCM of 9 and 5 is 45.

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 14 and 1 is 14.

The total number of girls and adults is 132 less than the number of boys.

Number of less girls and adults than the number of boys at first
= 36 u - 14 u
= 22 u

22 u = 132

1 u = 132 ÷ 22 = 6

Number of boys who entered the stadium
= 42 u - 36 u
= 6 u
= 6 x 6
= 36

Answer(s): 36