Ryan, Ethan and Julian had some marbles. Ethan had 25% less marbles than Ryan. Ethan had ²₇ of Julian's. After Ryan gave 100 marbles to Ethan, he had ¹₂ of what Ethan had. How many more marbles did Julian have than Ryan in the end?

Ryan	Ethan	Julian
4x2	3x2
	2x3	7x3
8	6	21

	Julian	Ryan	Ethan	Total marbles of  Ryan and Ethan
Before	21x3 = 63 u	8x3 = 24 u	6x3 = 18 u	14x3 = 42 u
Change		- 100	+ 100
After	63 u	1x14 = 14 u	2x14 = 28 u	3x14 = 42 u

Number of marbles that Ethan had less than Ryan at first in percent
= 100% - 25%
= 75%

75% = ⁷⁵₁₀₀ = ³₄

Ryan : Ethan = 4 : 3

The number of marbles that Ethan had at first is repeated.  Make the number of marbles that Ethan had at first the same.  LCM of 3 and 2 is 6.

When Ryan gave 100 marbles to Ethan, the total number of marbles that Ethan and Ryan had at first and in the end remains the same.  Make the total number of marbles that Ethan and Ryan had the same.  LCM of 14 and 3 is 42.

Number of marbles that Ryan gave to Ethan
= 24 u - 14 u
= 10 u

10 u = 100

1 u = 100 ÷ 10 = 10

Number of marbles that Julian had more than Ryan in the end
= 63 u - 14 u
= 49 u
= 49 x 10
= 490

Answer(s): 490