There were blue, grey and brown beads in a box. Sean put another 9 blue beads and 13 brown beads in the box, then the ratio of the number of grey beads to the number of brown beads became 5 : 2. Then, he doubled the number of blue beads and removed 20 brown beads. The ratio of the number of blue beads to grey beads became 2 : 1. He counted and found that there were a total of 133 beads left in the box. Find the number of blue beads that he had at first.

	Blue beads	Grey beads	Brown beads	Total
Before	5 u - 9	5 u	2 u - 13
Change 1	+ 9		+ 13
After 1	1x5 = 5 u	5 u	2 u
Change 2	+ 1x5 = 5 u		- 20
After 2	2x5 = 10 u	1x5 = 5 u	2 u - 20	133

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

Total number of beads in the end
= 10 u + 5 u + 2 u - 20
= 17 u - 20

17 u - 20 = 133
17 u = 133 + 20
17 u = 153

1 u = 153 ÷ 17 = 9

Number of blue beads at first
= 5 u - 9
= 5 x 9 - 9
= 45 - 9
= 36

Answer(s): 36