Reggie, Zeph and John had some balls. Zeph had 40% less balls than Reggie. Zeph had ⁴₇ of John's. After Reggie gave 72 balls to Zeph, he had ¹₃ of what Zeph had. How many more balls did John have than Reggie in the end?

Reggie	Zeph	John
5x4	3x4
	4x3	7x3
20	12	21

	John	Reggie	Zeph	Total balls of  Reggie and Zeph
Before	21x1 = 21 u	20x1 = 20 u	12x1 = 12 u	32x1 = 32 u
Change		- 72	+ 72
After	21 u	1x8 = 8 u	3x8 = 24 u	4x8 = 32 u

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

60% = ⁶⁰₁₀₀ = ³₅

Reggie : Zeph = 5 : 3

The number of balls that Zeph had at first is repeated.  Make the number of balls that Zeph had at first the same.  LCM of 3 and 4 is 12.

When Reggie gave 72 balls to Zeph, the total number of balls that Zeph and Reggie had at first and in the end remains the same.  Make the total number of balls that Zeph and Reggie had the same.  LCM of 32 and 4 is 32.

Number of balls that Reggie gave to Zeph
= 20 u - 8 u
= 12 u

12 u = 72

1 u = 72 ÷ 12 = 6

Number of balls that John had more than Reggie in the end
= 21 u - 8 u
= 13 u
= 13 x 6
= 78

Answer(s): 78