There were black, yellow and pink beads in a bottle. Sean put another 9 black beads and 12 pink beads in the bottle, then the ratio of the number of yellow beads to the number of pink beads became 5 : 2. Then, he doubled the number of black beads and removed 28 pink beads. The ratio of the number of black beads to yellow beads became 2 : 1. He counted and found that there were a total of 74 beads left in the bottle. Find the number of black beads that he had in the end.

	Black beads	Yellow beads	Pink beads	Total
Before	5 u - 9	5 u	2 u - 12
Change 1	+ 9		+ 12
After 1	1x5 = 5 u	5 u	2 u
Change 2	+ 1x5 = 5 u		- 28
After 2	2x5 = 10 u	1x5 = 5 u	2 u - 28	74

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

Total number of beads in the end
= 10 u + 5 u + 2 u - 28
= 17 u - 28

17 u - 28 = 74
17 u = 74 + 28
17 u = 102

1 u = 102 ÷ 17 = 6

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

Answer(s): 60