In a bottle, the ratio of the number of purple beads to the number of gold beads was 1 : 3. Each time, 3 purple and 7 gold beads were taken out of the bottle. A while later, only 160 gold beads were left in the bottle. What was the total number of beads in the bottle at first?

	Purple beads	Gold beads
Before	1x3 = 3 u	3x3 = 9 u
Change	- 3 u	- 7 u
After	0	160

Since there is no purple beads 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 beads at first and taken out the same.  LCM of 1 and 3 is 3.

Number of gold beads in the end
= 9 u - 7 u
= 2 u

2 u = 160

1 u = 160 ÷ 2 = 80

Total number of beads in the bottle at first
= 3 u + 9 u
= 12 u
= 12 x 80
= 960

Answer: 960