¹₉ of the visitors at a concert hall were girls. 80% of the remaining visitors were boys and the rest were adults. The total number of girls and adults is 380 less than the number of boys. After some boys entered the concert hall, 80% of the visitors that remained were boys. How many boys entered the concert hall?

Girls	Adults	Boys	Total
1x5	8x5		9x5
	1x8	4x8
5	8	32	45

	Girls and adults	Boys
Before	13x1 = 13 u	32x1 = 32 u
Change		+ 20 u
After	1x13 = 13 u	4x13 = 52 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 8 and 5 is 40.

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 13 and 1 is 13.

The total number of girls and adults is 380 less than the number of boys.

Number of less girls and adults than the number of boys at first
= 32 u - 13 u
= 19 u

19 u = 380

1 u = 380 ÷ 19 = 20

Number of boys who entered the concert hall
= 52 u - 32 u
= 20 u
= 20 x 20
= 400

Answer(s): 400