There were silver, brown and white beads in a container. Sean put another 3 silver beads and 15 white beads in the container, then the ratio of the number of brown beads to the number of white beads became 5 : 3. Then, he doubled the number of silver beads and removed 15 white beads. The ratio of the number of silver beads to brown beads became 2 : 1. He counted and found that there were a total of 93 beads left in the container. Find the number of silver beads that he had in the end.

	Silver beads	Brown beads	White beads	Total
Before	5 u - 3	5 u	3 u - 15
Change 1	+ 3		+ 15
After 1	1x5 = 5 u	5 u	3 u
Change 2	+ 1x5 = 5 u		- 15
After 2	2x5 = 10 u	1x5 = 5 u	3 u - 15	93

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 + 3 u - 15
= 18 u - 15

18 u - 15 = 93
18 u = 93 + 15
18 u = 108

1 u = 108 ÷ 18 = 6

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

Answer(s): 60