There were blue, green and yellow marbles in a jar. Sean put another 6 blue marbles and 14 yellow marbles in the jar, then the ratio of the number of green marbles to the number of yellow marbles became 4 : 3. Then, he doubled the number of blue marbles and removed 27 yellow marbles. The ratio of the number of blue marbles to green marbles became 2 : 1. He counted and found that there were a total of 33 marbles left in the jar. Find the number of blue marbles that he had in the end.

	Blue marbles	Green marbles	Yellow marbles	Total
Before	4 u - 6	4 u	3 u - 14
Change 1	+ 6		+ 14
After 1	1x4 = 4 u	4 u	3 u
Change 2	+ 1x4 = 4 u		- 27
After 2	2x4 = 8 u	1x4 = 4 u	3 u - 27	33

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

Total number of marbles in the end
= 8 u + 4 u + 3 u - 27
= 15 u - 27

15 u - 27 = 33
15 u = 33 + 27
15 u = 60

1 u = 60 ÷ 15 = 4

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

Answer(s): 32