There were white, black and purple marbles in a box. Sean put another 9 white marbles and 15 purple marbles in the box, then the ratio of the number of black marbles to the number of purple marbles became 4 : 3. Then, he doubled the number of white marbles and removed 12 purple marbles. The ratio of the number of white marbles to black marbles became 2 : 1. He counted and found that there were a total of 78 marbles left in the box. Find the number of white marbles that he had in the end.

	White marbles	Black marbles	Purple marbles	Total
Before	4 u - 9	4 u	3 u - 15
Change 1	+ 9		+ 15
After 1	1x4 = 4 u	4 u	3 u
Change 2	+ 1x4 = 4 u		- 12
After 2	2x4 = 8 u	1x4 = 4 u	3 u - 12	78

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

Total number of marbles in the end
= 8 u + 4 u + 3 u - 12
= 15 u - 12

15 u - 12 = 78
15 u = 78 + 12
15 u = 90

1 u = 90 ÷ 15 = 6

Number of white marbles in the end
= 8 u 
= 8 x 6
= 48

Answer(s): 48