In a tin can, the ratio of the number of purple beads to the number of white beads was 1 : 4. Each time, 4 purple and 6 white beads were taken out of the tin can. A while later, only 180 white beads were left in the tin can. What was the total number of beads in the tin can at first?

	Purple beads	White beads
Before	1x4 = 4 u	4x4 = 16 u
Change	- 4 u	- 6 u
After	0	180

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 4 is 4.

Number of white beads in the end
= 16 u - 6 u
= 10 u

10 u = 180

1 u = 180 ÷ 10 = 18

Total number of beads in the tin can at first
= 4 u + 16 u
= 20 u
= 20 x 18
= 360

Answer: 360