¹₈ of the people at a museum were girls. 80% of the remaining people were boys and the rest were adults. The total number of girls and adults is 128 less than the number of boys. After some boys entered the museum, 80% of the people that remained were boys. How many boys entered the museum?

Girls	Adults	Boys	Total
1x5	7x5		8x5
	1x7	4x7
5	7	28	40

	Girls and adults	Boys
Before	12x1 = 12 u	28x1 = 28 u
Change		+ 20 u
After	1x12 = 12 u	4x12 = 48 u

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

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 5 is 35.

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 12 and 1 is 12.

The total number of girls and adults is 128 less than the number of boys.

Number of less girls and adults than the number of boys at first
= 28 u - 12 u
= 16 u

16 u = 128

1 u = 128 ÷ 16 = 8

Number of boys who entered the museum
= 48 u - 28 u
= 20 u
= 20 x 8
= 160

Answer(s): 160