There were yellow, brown and purple beads in a jar. Sean put another 8 yellow beads and 15 purple beads in the jar, then the ratio of the number of brown beads to the number of purple beads became 5 : 2. Then, he doubled the number of yellow beads and removed 11 purple beads. The ratio of the number of yellow beads to brown beads became 2 : 1. He counted and found that there were a total of 57 beads left in the jar. Find the number of yellow beads that he had at first.

	Yellow beads	Brown beads	Purple beads	Total
Before	5 u - 8	5 u	2 u - 15
Change 1	+ 8		+ 15
After 1	1x5 = 5 u	5 u	2 u
Change 2	+ 1x5 = 5 u		- 11
After 2	2x5 = 10 u	1x5 = 5 u	2 u - 11	57

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 - 11
= 17 u - 11

17 u - 11 = 57
17 u = 57 + 11
17 u = 68

1 u = 68 ÷ 17 = 4

Number of yellow beads at first
= 5 u - 8
= 5 x 4 - 8
= 20 - 8
= 12

Answer(s): 12