Cole, Charlie and Ethan had some marbles. Charlie had 40% more marbles than Cole. Charlie had ³₇ of Ethan's. After Cole gave 30 marbles to Charlie, he had ¹₃ of what Charlie had. How many more marbles did Ethan have than Charlie in the end?

Cole	Charlie	Ethan
5x3	7x3
	3x7	7x7
15	21	49

	Ethan	Cole	Charlie	Total marbles of  Cole and Charlie
Before	49x1 = 49 u	15x1 = 15 u	21x1 = 21 u	36x1 = 36 u
Change		- 30	+ 30
After	49 u	1x9 = 9 u	3x9 = 27 u	4x9 = 36 u

Number of marbles that Charlie had more than Cole at first in percent
= 100%+ 40%
= 140%

140% = ¹⁴⁰₁₀₀ = ⁷₅

Cole : Charlie = 5 : 7

The number of marbles that Charlie had at first is repeated.  Make the number of marbles that Charlie had at first the same.  LCM of 7 and 3 is 21.

When Cole gave 30 marbles to Charlie, the total number of marbles that Charlie and Cole had at first and in the end remains the same.  Make the total number of marbles that Charlie and Cole had the same.  LCM of 36 and 4 is 36.

Number of marbles that Cole gave to Charlie
= 15 u - 9 u
= 6 u

6 u = 30

1 u = 30 ÷ 6 = 5

Number of marbles that Ethan had more than Charlie in the end
= 49 u - 27 u
= 22 u
= 22 x 5
= 110

Answer(s): 110