There were brown, white and blue beads in a bottle. Sean put another 10 brown beads and 7 blue beads in the bottle, then the ratio of the number of white beads to the number of blue beads became 5 : 3. Then, he doubled the number of brown beads and removed 21 blue beads. The ratio of the number of brown beads to white beads became 2 : 1. He counted and found that there were a total of 105 beads left in the bottle. Find the number of brown beads that he had in the end.

	Brown beads	White beads	Blue beads	Total
Before	5 u - 10	5 u	3 u - 7
Change 1	+ 10		+ 7
After 1	1x5 = 5 u	5 u	3 u
Change 2	+ 1x5 = 5 u		- 21
After 2	2x5 = 10 u	1x5 = 5 u	3 u - 21	105

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

Total number of beads in the end
= 10 u + 5 u + 3 u - 21
= 18 u - 21

18 u - 21 = 105
18 u = 105 + 21
18 u = 126

1 u = 126 ÷ 18 = 7

Number of brown beads in the end
= 10 u 
= 10 x 7
= 70

Answer(s): 70