Fred, Justin and Ethan had some balls. Justin had 60% less balls than Fred. Justin had ⁴₇ of Ethan's. After Fred gave 39 balls to Justin, he had ¹₃ of what Justin had. How many more balls did Ethan have than Fred in the end?

Fred	Justin	Ethan
5x2	2x2
	4x1	7x1
10	4	7

	Ethan	Fred	Justin	Total balls of  Fred and Justin
Before	7x2 = 14 u	10x2 = 20 u	4x2 = 8 u	14x2 = 28 u
Change		- 39	+ 39
After	14 u	1x7 = 7 u	3x7 = 21 u	4x7 = 28 u

Number of balls that Justin had less than Fred at first in percent
= 100% - 60%
= 40%

40% = ⁴⁰₁₀₀ = ²₅

Fred : Justin = 5 : 2

The number of balls that Justin had at first is repeated.  Make the number of balls that Justin had at first the same.  LCM of 2 and 4 is 4.

When Fred gave 39 balls to Justin, the total number of balls that Justin and Fred had at first and in the end remains the same.  Make the total number of balls that Justin and Fred had the same.  LCM of 14 and 4 is 28.

Number of balls that Fred gave to Justin
= 20 u - 7 u
= 13 u

13 u = 39

1 u = 39 ÷ 13 = 3

Number of balls that Ethan had more than Fred in the end
= 14 u - 7 u
= 7 u
= 7 x 3
= 21

Answer(s): 21