¹₉ of the guests at a zoo were boys. 70% of the remaining guests were girls and the rest were adults. The total number of boys and adults is 209 less than the number of girls. After some girls entered the zoo, 80% of the guests that remained were girls. How many girls entered the zoo?

Boys	Adults	Girls	Total
1x5	8x5		9x5
	3x4	7x4
5	12	28	45

	Boys and adults	Girls
Before	17x1 = 17 u	28x1 = 28 u
Change		+ 40 u
After	1x17 = 17 u	4x17 = 68 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 8 and 10 is 40.

80% = ⁸⁰₁₀₀ = ⁴₅

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 17 and 1 is 17.

The total number of boys and adults is 209 less than the number of girls.

Number of less boys and adults than the number of girls at first
= 28 u - 17 u
= 11 u

11 u = 209

1 u = 209 ÷ 11 = 19

Number of girls who entered the zoo
= 68 u - 28 u
= 40 u
= 40 x 19
= 760

Answer(s): 760