There were brown, purple and white marbles in a container. Sean put another 5 brown marbles and 4 white marbles in the container, then the ratio of the number of purple marbles to the number of white marbles became 5 : 3. Then, he doubled the number of brown marbles and removed 27 white marbles. The ratio of the number of brown marbles to purple marbles became 2 : 1. He counted and found that there were a total of 27 marbles left in the container. Find the number of brown marbles that he had at first.

	Brown marbles	Purple marbles	White marbles	Total
Before	5 u - 5	5 u	3 u - 4
Change 1	+ 5		+ 4
After 1	1x5 = 5 u	5 u	3 u
Change 2	+ 1x5 = 5 u		- 27
After 2	2x5 = 10 u	1x5 = 5 u	3 u - 27	27

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

Total number of marbles in the end
= 10 u + 5 u + 3 u - 27
= 18 u - 27

18 u - 27 = 27
18 u = 27 + 27
18 u = 54

1 u = 54 ÷ 18 = 3

Number of brown marbles at first
= 5 u - 5
= 5 x 3 - 5
= 15 - 5
= 10

Answer(s): 10