²₉ of the guests at a stadium were boys. 80% of the remaining guests were girls and the rest were adults. The total number of boys and adults is 154 less than the number of girls. After some girls entered the stadium, 80% of the guests that remained were girls. How many girls entered the stadium?

Boys	Adults	Girls	Total
2x5	7x5		9x5
	1x7	4x7
10	7	28	45

	Boys and adults	Girls
Before	17x1 = 17 u	28x1 = 28 u
Change		+ 40 u
After	1x17 = 17 u	4x17 = 68 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 7 and 5 is 35.

80% = ⁸⁰₁₀₀ = ⁴₅

When some girls entered, the total number of boys and adults remains unchanged. Make the total number of boys and adults the same. LCM of 17 and 1 is 17.

The total number of boys and adults is 154 less than the number of girls.

Number of less boys and adults than the number of girls at first
= 28 u - 17 u
= 11 u

11 u = 154

1 u = 154 ÷ 11 = 14

Number of girls who entered the stadium
= 68 u - 28 u
= 40 u
= 40 x 14
= 560

Answer(s): 560