There were black, purple and grey marbles in a box. Sean put another 8 black marbles and 6 grey marbles in the box, then the ratio of the number of purple marbles to the number of grey marbles became 4 : 3. Then, he doubled the number of black marbles and removed 16 grey marbles. The ratio of the number of black marbles to purple marbles became 2 : 1. He counted and found that there were a total of 29 marbles left in the box. Find the number of black marbles that he had in the end.

	Black marbles	Purple marbles	Grey marbles	Total
Before	4 u - 8	4 u	3 u - 6
Change 1	+ 8		+ 6
After 1	1x4 = 4 u	4 u	3 u
Change 2	+ 1x4 = 4 u		- 16
After 2	2x4 = 8 u	1x4 = 4 u	3 u - 16	29

The number of purple marbles remains unchanged. Make the number of purple marbles the same. LCM of 1 and 4 is 4.

Total number of marbles in the end
= 8 u + 4 u + 3 u - 16
= 15 u - 16

15 u - 16 = 29
15 u = 29 + 16
15 u = 45

1 u = 45 ÷ 15 = 3

Number of black marbles in the end
= 8 u 
= 8 x 3
= 24

Answer(s): 24