In a tin can, the ratio of the number of purple balls to the number of grey balls was 1 : 4. Each time, 3 purple and 7 grey balls were taken out of the tin can. A while later, only 125 grey balls were left in the tin can. What was the total number of balls in the tin can at first?

	Purple balls	Grey balls
Before	1x3 = 3 u	4x3 = 12 u
Change	- 3 u	- 7 u
After	0	125

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

Number of grey balls in the end
= 12 u - 7 u
= 5 u

5 u = 125

1 u = 125 ÷ 5 = 25

Total number of balls in the tin can at first
= 3 u + 12 u
= 15 u
= 15 x 25
= 375

Answer: 375