²₉ of the visitors at a theme park were girls. 90% of the remaining visitors were boys and the rest were adults. The number of boys was 540 more than the total number of girls and adults. After some boys left the theme park, 50% of the visitors that remained were boys. How many boys left the theme park?

Girls	Adults	Boys	Total
2x10	7x10		9x10
	1x7	9x7
20	7	63	90

	Girls and adults	Boys
Before	27x1 = 27 u	63x1 = 63 u
Change		- 36 u
After	1x27 = 27 u	1x27 = 27 u

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

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 10 is 70.

50% = ⁵⁰₁₀₀ = ¹₂

When some boys left, the total number of girls and adults remains unchanged. Make the total number of girls and adults the same. LCM of 27 and 1 is 27.

The number of boys was 540 more than the total number of girls and adults at first.

Number of more boys than the total number of girls and adults at first
= 63 u - 27 u
= 36 u

36 u = 540

1 u = 540 ÷ 36 = 15

Number of boys who left the theme park
= 63 u - 27 u
= 36 u
= 36 x 15
= 540

Answer(s): 540