Valen, Ethan and Jack had some marbles. Ethan had 60% less marbles than Valen. Ethan had ³₈ of Jack's. After Valen gave 276 marbles to Ethan, he had ¹₅ of what Ethan had. How many more marbles did Jack have than Valen in the end?

Valen	Ethan	Jack
5x3	2x3
	3x2	8x2
15	6	16

	Jack	Valen	Ethan	Total marbles of  Valen and Ethan
Before	16x2 = 32 u	15x2 = 30 u	6x2 = 12 u	21x2 = 42 u
Change		- 276	+ 276
After	32 u	1x7 = 7 u	5x7 = 35 u	6x7 = 42 u

Number of marbles that Ethan had less than Valen at first in percent
= 100% - 60%
= 40%

40% = ⁴⁰₁₀₀ = ²₅

Valen : Ethan = 5 : 2

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 2 and 3 is 6.

When Valen gave 276 marbles to Ethan, the total number of marbles that Ethan and Valen had at first and in the end remains the same.  Make the total number of marbles that Ethan and Valen had the same.  LCM of 21 and 6 is 42.

Number of marbles that Valen gave to Ethan
= 30 u - 7 u
= 23 u

23 u = 276

1 u = 276 ÷ 23 = 12

Number of marbles that Jack had more than Valen in the end
= 32 u - 7 u
= 25 u
= 25 x 12
= 300

Answer(s): 300