Henry, Luke and Gabriel had some marbles. Luke had 80% less marbles than Henry. Luke had ³₇ of Gabriel's. After Henry gave 81 marbles to Luke, he had ¹₂ of what Luke had. How many more marbles did Gabriel have than Henry in the end?

Henry	Luke	Gabriel
5x3	1x3
	3x1	7x1
15	3	7

	Gabriel	Henry	Luke	Total marbles of  Henry and Luke
Before	7x1 = 7 u	15x1 = 15 u	3x1 = 3 u	18x1 = 18 u
Change		- 81	+ 81
After	7 u	1x6 = 6 u	2x6 = 12 u	3x6 = 18 u

Number of marbles that Luke had less than Henry at first in percent
= 100% - 80%
= 20%

20% = ²⁰₁₀₀ = ¹₅

Henry : Luke = 5 : 1

The number of marbles that Luke had at first is repeated.  Make the number of marbles that Luke had at first the same.  LCM of 1 and 3 is 3.

When Henry gave 81 marbles to Luke, the total number of marbles that Luke and Henry had at first and in the end remains the same.  Make the total number of marbles that Luke and Henry had the same.  LCM of 18 and 3 is 18.

Number of marbles that Henry gave to Luke
= 15 u - 6 u
= 9 u

9 u = 81

1 u = 81 ÷ 9 = 9

Number of marbles that Gabriel had more than Henry in the end
= 7 u - 6 u
= 1 u
= 1 x 9
= 9

Answer(s): 9