¹₈ of the guests at a safari park were girls. 75% of the remaining guests were boys and the rest were adults. The total number of girls and adults is 170 less than the number of boys. After some boys entered the safari park, 80% of the guests that remained were boys. How many boys entered the safari park?

Girls	Adults	Boys	Total
1x4	7x4		8x4
	1x7	3x7
4	7	21	32

	Girls and adults	Boys
Before	11x1 = 11 u	21x1 = 21 u
Change		+ 23 u
After	1x11 = 11 u	4x11 = 44 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 7 and 4 is 28.

80% = ⁸⁰₁₀₀ = ⁴₅

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 11 and 1 is 11.

The total number of girls and adults is 170 less than the number of boys.

Number of less girls and adults than the number of boys at first
= 21 u - 11 u
= 10 u

10 u = 170

1 u = 170 ÷ 10 = 17

Number of boys who entered the safari park
= 44 u - 21 u
= 23 u
= 23 x 17
= 391

Answer(s): 391