There were blue, gold and silver marbles in a container. Sean put another 3 blue marbles and 12 silver marbles in the container, then the ratio of the number of gold marbles to the number of silver marbles became 4 : 3. Then, he doubled the number of blue marbles and removed 22 silver marbles. The ratio of the number of blue marbles to gold marbles became 2 : 1. He counted and found that there were a total of 68 marbles left in the container. Find the number of blue marbles that he had at first.

	Blue marbles	Gold marbles	Silver marbles	Total
Before	4 u - 3	4 u	3 u - 12
Change 1	+ 3		+ 12
After 1	1x4 = 4 u	4 u	3 u
Change 2	+ 1x4 = 4 u		- 22
After 2	2x4 = 8 u	1x4 = 4 u	3 u - 22	68

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

Total number of marbles in the end
= 8 u + 4 u + 3 u - 22
= 15 u - 22

15 u - 22 = 68
15 u = 68 + 22
15 u = 90

1 u = 90 ÷ 15 = 6

Number of blue marbles at first
= 4 u - 3
= 4 x 6 - 3
= 24 - 3
= 21

Answer(s): 21