There were grey, pink and brown marbles in a container. Sean put another 3 grey marbles and 12 brown marbles in the container, then the ratio of the number of pink marbles to the number of brown marbles became 6 : 5. Then, he doubled the number of grey marbles and removed 10 brown marbles. The ratio of the number of grey marbles to pink marbles became 2 : 1. He counted and found that there were a total of 82 marbles left in the container. Find the number of grey marbles that he had at first.

	Grey marbles	Pink marbles	Brown marbles	Total
Before	6 u - 3	6 u	5 u - 12
Change 1	+ 3		+ 12
After 1	1x6 = 6 u	6 u	5 u
Change 2	+ 1x6 = 6 u		- 10
After 2	2x6 = 12 u	1x6 = 6 u	5 u - 10	82

The number of pink marbles remains unchanged. Make the number of pink marbles the same. LCM of 1 and 6 is 6.

Total number of marbles in the end
= 12 u + 6 u + 5 u - 10
= 23 u - 10

23 u - 10 = 82
23 u = 82 + 10
23 u = 92

1 u = 92 ÷ 23 = 4

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

Answer(s): 21