¹₁₀ of the guests at a bird park were girls. 75% of the remaining guests were boys and the rest were adults. The total number of girls and adults is 168 less than the number of boys. After some boys entered the bird park, 75% of the guests that remained were boys. How many boys entered the bird park?

Girls	Adults	Boys	Total
1x4	9x4		10x4
	1x9	3x9
4	9	27	40

	Girls and adults	Boys
Before	13x1 = 13 u	27x1 = 27 u
Change		+ 12 u
After	1x13 = 13 u	3x13 = 39 u

75% = ⁷⁵₁₀₀ = ³₄
Adults : Boys = 1 : 3

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 4 is 36.

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 13 and 1 is 13.

The total number of girls and adults is 168 less than the number of boys.

Number of less girls and adults than the number of boys at first
= 27 u - 13 u
= 14 u

14 u = 168

1 u = 168 ÷ 14 = 12

Number of boys who entered the bird park
= 39 u - 27 u
= 12 u
= 12 x 12
= 144

Answer(s): 144