²₉ of the people at a park were girls. 80% of the remaining people were boys and the rest were adults. The total number of girls and adults is 132 less than the number of boys. After some boys entered the park, 80% of the people that remained were boys. How many boys entered the park?

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

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

The total number of girls and adults is 132 less than the number of boys.

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

11 u = 132

1 u = 132 ÷ 11 = 12

Number of boys who entered the park
= 68 u - 28 u
= 40 u
= 40 x 12
= 480

Answer(s): 480