In a bottle, the ratio of the number of purple marbles to the number of white marbles was 1 : 3. Each time, 4 purple and 6 white marbles were taken out of the bottle. A while later, only 168 white marbles were left in the bottle. What was the total number of marbles in the bottle at first?

	Purple marbles	White marbles
Before	1x4 = 4 u	3x4 = 12 u
Change	- 4 u	- 6 u
After	0	168

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 4 is 4.

Number of white marbles in the end
= 12 u - 6 u
= 6 u

6 u = 168

1 u = 168 ÷ 6 = 28

Total number of marbles in the bottle at first
= 4 u + 12 u
= 16 u
= 16 x 28
= 448

Answer: 448