There were pink, red and purple marbles in a container. Sean put another 6 pink marbles and 9 purple marbles in the container, then the ratio of the number of red marbles to the number of purple marbles became 5 : 3. Then, he doubled the number of pink marbles and removed 27 purple marbles. The ratio of the number of pink marbles to red marbles became 2 : 1. He counted and found that there were a total of 99 marbles left in the container. Find the number of pink marbles that he had in the end.

	Pink marbles	Red marbles	Purple marbles	Total
Before	5 u - 6	5 u	3 u - 9
Change 1	+ 6		+ 9
After 1	1x5 = 5 u	5 u	3 u
Change 2	+ 1x5 = 5 u		- 27
After 2	2x5 = 10 u	1x5 = 5 u	3 u - 27	99

The number of red marbles remains unchanged. Make the number of red marbles the same. LCM of 1 and 5 is 5.

Total number of marbles in the end
= 10 u + 5 u + 3 u - 27
= 18 u - 27

18 u - 27 = 99
18 u = 99 + 27
18 u = 126

1 u = 126 ÷ 18 = 7

Number of pink marbles in the end
= 10 u 
= 10 x 7
= 70

Answer(s): 70