There were white, purple and red marbles in a jar. Sean put another 4 white marbles and 13 red marbles in the jar, then the ratio of the number of purple marbles to the number of red marbles became 4 : 3. Then, he doubled the number of white marbles and removed 14 red marbles. The ratio of the number of white marbles to purple marbles became 2 : 1. He counted and found that there were a total of 76 marbles left in the jar. Find the number of white marbles that he had in the end.

	White marbles	Purple marbles	Red marbles	Total
Before	4 u - 4	4 u	3 u - 13
Change 1	+ 4		+ 13
After 1	1x4 = 4 u	4 u	3 u
Change 2	+ 1x4 = 4 u		- 14
After 2	2x4 = 8 u	1x4 = 4 u	3 u - 14	76

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 - 14
= 15 u - 14

15 u - 14 = 76
15 u = 76 + 14
15 u = 90

1 u = 90 ÷ 15 = 6

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

Answer(s): 48