There were black, silver and green marbles in a box. Sean put another 8 black marbles and 3 green marbles in the box, then the ratio of the number of silver marbles to the number of green marbles became 4 : 3. Then, he doubled the number of black marbles and removed 19 green marbles. The ratio of the number of black marbles to silver marbles became 2 : 1. He counted and found that there were a total of 41 marbles left in the box. Find the number of black marbles that he had in the end.

	Black marbles	Silver marbles	Green marbles	Total
Before	4 u - 8	4 u	3 u - 3
Change 1	+ 8		+ 3
After 1	1x4 = 4 u	4 u	3 u
Change 2	+ 1x4 = 4 u		- 19
After 2	2x4 = 8 u	1x4 = 4 u	3 u - 19	41

The number of silver marbles remains unchanged. Make the number of silver marbles the same. LCM of 1 and 4 is 4.

Total number of marbles in the end
= 8 u + 4 u + 3 u - 19
= 15 u - 19

15 u - 19 = 41
15 u = 41 + 19
15 u = 60

1 u = 60 ÷ 15 = 4

Number of black marbles in the end
= 8 u 
= 8 x 4
= 32

Answer(s): 32