¹₁₀ of the guests at a park were boys. 90% of the remaining guests were girls and the rest were adults. The number of girls was 434 more than the total number of boys and adults. After some girls left the park, 50% of the guests that remained were girls. How many girls left the park?

Boys	Adults	Girls	Total
1x10	9x10		10x10
	1x9	9x9
10	9	81	100

	Boys and adults	Girls
Before	19x1 = 19 u	81x1 = 81 u
Change		- 62 u
After	1x19 = 19 u	1x19 = 19 u

90% = ⁹⁰₁₀₀ = ⁹₁₀
Adults : Girls = 1 : 9

The total number of adults and girls at first is repeated.  Make the total number of adults at first the same. LCM of 9 and 10 is 90.

50% = ⁵⁰₁₀₀ = ¹₂

When some girls left, the total number of boys and adults remains unchanged. Make the total number of boys and adults the same. LCM of 19 and 1 is 19.

The number of girls was 434 more than the total number of boys and adults at first.

Number of more girls than the total number of boys and adults at first
= 81 u - 19 u
= 62 u

62 u = 434

1 u = 434 ÷ 62 = 7

Number of girls who left the park
= 81 u - 19 u
= 62 u
= 62 x 7
= 434

Answer(s): 434