There were grey, red and black beads in a box. Sean put another 6 grey beads and 14 black beads in the box, then the ratio of the number of red beads to the number of black beads became 4 : 3. Then, he doubled the number of grey beads and removed 30 black beads. The ratio of the number of grey beads to red beads became 2 : 1. He counted and found that there were a total of 15 beads left in the box. Find the number of grey beads that he had in the end.

	Grey beads	Red beads	Black beads	Total
Before	4 u - 6	4 u	3 u - 14
Change 1	+ 6		+ 14
After 1	1x4 = 4 u	4 u	3 u
Change 2	+ 1x4 = 4 u		- 30
After 2	2x4 = 8 u	1x4 = 4 u	3 u - 30	15

The number of red beads remains unchanged. Make the number of red beads the same. LCM of 1 and 4 is 4.

Total number of beads in the end
= 8 u + 4 u + 3 u - 30
= 15 u - 30

15 u - 30 = 15
15 u = 15 + 30
15 u = 45

1 u = 45 ÷ 15 = 3

Number of grey beads in the end
= 8 u 
= 8 x 3
= 24

Answer(s): 24