There were blue, brown and gold beads in a box. Sean put another 4 blue beads and 15 gold beads in the box, then the ratio of the number of brown beads to the number of gold beads became 5 : 2. Then, he doubled the number of blue beads and removed 13 gold beads. The ratio of the number of blue beads to brown beads became 2 : 1. He counted and found that there were a total of 89 beads left in the box. Find the number of blue beads that he had in the end.

	Blue beads	Brown beads	Gold beads	Total
Before	5 u - 4	5 u	2 u - 15
Change 1	+ 4		+ 15
After 1	1x5 = 5 u	5 u	2 u
Change 2	+ 1x5 = 5 u		- 13
After 2	2x5 = 10 u	1x5 = 5 u	2 u - 13	89

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

Total number of beads in the end
= 10 u + 5 u + 2 u - 13
= 17 u - 13

17 u - 13 = 89
17 u = 89 + 13
17 u = 102

1 u = 102 ÷ 17 = 6

Number of blue beads in the end
= 10 u 
= 10 x 6
= 60

Answer(s): 60