Henry, John and Zane had some marbles. John had 60% less marbles than Henry. John had ⁴₇ of Zane's. After Henry gave 138 marbles to John, he had ¹₅ of what John had. How many more marbles did Zane have than Henry in the end?

Henry	John	Zane
5x2	2x2
	4x1	7x1
10	4	7

	Zane	Henry	John	Total marbles of  Henry and John
Before	7x3 = 21 u	10x3 = 30 u	4x3 = 12 u	14x3 = 42 u
Change		- 138	+ 138
After	21 u	1x7 = 7 u	5x7 = 35 u	6x7 = 42 u

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

40% = ⁴⁰₁₀₀ = ²₅

Henry : John = 5 : 2

The number of marbles that John had at first is repeated.  Make the number of marbles that John had at first the same.  LCM of 2 and 4 is 4.

When Henry gave 138 marbles to John, the total number of marbles that John and Henry had at first and in the end remains the same.  Make the total number of marbles that John and Henry had the same.  LCM of 14 and 6 is 42.

Number of marbles that Henry gave to John
= 30 u - 7 u
= 23 u

23 u = 138

1 u = 138 ÷ 23 = 6

Number of marbles that Zane had more than Henry in the end
= 21 u - 7 u
= 14 u
= 14 x 6
= 84

Answer(s): 84