There were green, red and yellow marbles in a bottle. Sean put another 10 green marbles and 15 yellow marbles in the bottle, then the ratio of the number of red marbles to the number of yellow marbles became 5 : 2. Then, he doubled the number of green marbles and removed 17 yellow marbles. The ratio of the number of green marbles to red marbles became 2 : 1. He counted and found that there were a total of 51 marbles left in the bottle. Find the number of green marbles that he had in the end.

	Green marbles	Red marbles	Yellow marbles	Total
Before	5 u - 10	5 u	2 u - 15
Change 1	+ 10		+ 15
After 1	1x5 = 5 u	5 u	2 u
Change 2	+ 1x5 = 5 u		- 17
After 2	2x5 = 10 u	1x5 = 5 u	2 u - 17	51

The number of red marbles remains unchanged. Make the number of red marbles the same. LCM of 1 and 5 is 5.

Total number of marbles in the end
= 10 u + 5 u + 2 u - 17
= 17 u - 17

17 u - 17 = 51
17 u = 51 + 17
17 u = 68

1 u = 68 ÷ 17 = 4

Number of green marbles in the end
= 10 u 
= 10 x 4
= 40

Answer(s): 40