There were purple, gold and pink marbles in a bottle. Sean put another 3 purple marbles and 9 pink marbles in the bottle, then the ratio of the number of gold marbles to the number of pink marbles became 5 : 3. Then, he doubled the number of purple marbles and removed 25 pink marbles. The ratio of the number of purple marbles to gold marbles became 2 : 1. He counted and found that there were a total of 29 marbles left in the bottle. Find the number of purple marbles that he had at first.

	Purple marbles	Gold marbles	Pink marbles	Total
Before	5 u - 3	5 u	3 u - 9
Change 1	+ 3		+ 9
After 1	1x5 = 5 u	5 u	3 u
Change 2	+ 1x5 = 5 u		- 25
After 2	2x5 = 10 u	1x5 = 5 u	3 u - 25	29

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

Total number of marbles in the end
= 10 u + 5 u + 3 u - 25
= 18 u - 25

18 u - 25 = 29
18 u = 29 + 25
18 u = 54

1 u = 54 ÷ 18 = 3

Number of purple marbles at first
= 5 u - 3
= 5 x 3 - 3
= 15 - 3
= 12

Answer(s): 12