¹₁₀ of the people at a museum were boys. 80% of the remaining people were girls and the rest were adults. The number of girls was 1056 more than the total number of boys and adults. After some girls left the museum, 70% of the people that remained were girls. How many girls left the museum?

Boys	Adults	Girls	Total
1x5	9x5		10x5
	1x9	4x9
5	9	36	50

	Boys and adults	Girls
Before	14x3 = 42 u	36x3 = 108 u
Change		- 10 u
After	3x14 = 42 u	7x14 = 98 u

80% = ⁸⁰₁₀₀ = ⁴₅
Adults : Girls = 1 : 4

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 5 is 45.

70% = ⁷⁰₁₀₀ = ⁷₁₀

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 14 and 3 is 42.

The number of girls was 1056 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
= 108 u - 42 u
= 66 u

66 u = 1056

1 u = 1056 ÷ 66 = 16

Number of girls who left the museum
= 108 u - 98 u
= 10 u
= 10 x 16
= 160

Answer(s): 160