There were black, white and purple marbles in a container. Sean put another 8 black marbles and 4 purple marbles in the container, then the ratio of the number of white marbles to the number of purple marbles became 5 : 3. Then, he doubled the number of black marbles and removed 13 purple marbles. The ratio of the number of black marbles to white marbles became 2 : 1. He counted and found that there were a total of 149 marbles left in the container. Find the number of black marbles that he had at first.

	Black marbles	White marbles	Purple marbles	Total
Before	5 u - 8	5 u	3 u - 4
Change 1	+ 8		+ 4
After 1	1x5 = 5 u	5 u	3 u
Change 2	+ 1x5 = 5 u		- 13
After 2	2x5 = 10 u	1x5 = 5 u	3 u - 13	149

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

Total number of marbles in the end
= 10 u + 5 u + 3 u - 13
= 18 u - 13

18 u - 13 = 149
18 u = 149 + 13
18 u = 162

1 u = 162 ÷ 18 = 9

Number of black marbles at first
= 5 u - 8
= 5 x 9 - 8
= 45 - 8
= 37

Answer(s): 37