In a tin can, the ratio of the number of purple marbles to the number of grey marbles was 1 : 3. Each time, 3 purple and 6 grey marbles were taken out of the tin can. A while later, only 144 grey marbles were left in the tin can. What was the total number of marbles in the tin can at first?

	Purple marbles	Grey marbles
Before	1x3 = 3 u	3x3 = 9 u
Change	- 3 u	- 6 u
After	0	144

Since there is no purple marbles left, this means that the number of purple marbles at first is the same as the number of purple marbles taken out.  

Make the number of purple marbles at first and taken out the same.  LCM of 1 and 3 is 3.

Number of grey marbles in the end
= 9 u - 6 u
= 3 u

3 u = 144

1 u = 144 ÷ 3 = 48

Total number of marbles in the tin can at first
= 3 u + 9 u
= 12 u
= 12 x 48
= 576

Answer: 576