Caden, Bryan and Gabriel had some balls. Bryan had 20% more balls than Caden. Bryan had ³₈ of Gabriel's. After Caden gave 63 balls to Bryan, he had ¹₃ of what Bryan had. How many more balls did Gabriel have than Bryan in the end?

Caden	Bryan	Gabriel
5x1	6x1
	3x2	8x2
5	6	16

	Gabriel	Caden	Bryan	Total balls of  Caden and Bryan
Before	16x4 = 64 u	5x4 = 20 u	6x4 = 24 u	11x4 = 44 u
Change		- 63	+ 63
After	64 u	1x11 = 11 u	3x11 = 33 u	4x11 = 44 u

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

120% = ¹²⁰₁₀₀ = ⁶₅

Caden : Bryan = 5 : 6

The number of balls that Bryan had at first is repeated.  Make the number of balls that Bryan had at first the same.  LCM of 6 and 3 is 6.

When Caden gave 63 balls to Bryan, the total number of balls that Bryan and Caden had at first and in the end remains the same.  Make the total number of balls that Bryan and Caden had the same.  LCM of 11 and 4 is 44.

Number of balls that Caden gave to Bryan
= 20 u - 11 u
= 9 u

9 u = 63

1 u = 63 ÷ 9 = 7

Number of balls that Gabriel had more than Bryan in the end
= 64 u - 33 u
= 31 u
= 31 x 7
= 217

Answer(s): 217