Elijah, Michael and Ethan had some balls. Michael had 20% more balls than Elijah. Michael had ²₅ of Ethan's. After Elijah gave 8 balls to Michael, he had ¹₂ of what Michael had. How many more balls did Ethan have than Michael in the end?

Elijah	Michael	Ethan
5x1	6x1
	2x3	5x3
5	6	15

	Ethan	Elijah	Michael	Total balls of  Elijah and Michael
Before	15x3 = 45 u	5x3 = 15 u	6x3 = 18 u	11x3 = 33 u
Change		- 8	+ 8
After	45 u	1x11 = 11 u	2x11 = 22 u	3x11 = 33 u

Number of balls that Michael had more than Elijah at first in percent
= 100%+ 20%
= 120%

120% = ¹²⁰₁₀₀ = ⁶₅

Elijah : Michael = 5 : 6

The number of balls that Michael had at first is repeated.  Make the number of balls that Michael had at first the same.  LCM of 6 and 2 is 6.

When Elijah gave 8 balls to Michael, the total number of balls that Michael and Elijah had at first and in the end remains the same.  Make the total number of balls that Michael and Elijah had the same.  LCM of 11 and 3 is 33.

Number of balls that Elijah gave to Michael
= 15 u - 11 u
= 4 u

4 u = 8

1 u = 8 ÷ 4 = 2

Number of balls that Ethan had more than Michael in the end
= 45 u - 22 u
= 23 u
= 23 x 2
= 46

Answer(s): 46