In a tin can, the ratio of the number of purple balls to the number of gold balls was 1 : 4. Each time, 3 purple and 6 gold balls were taken out of the tin can. A while later, only 186 gold balls were left in the tin can. What was the total number of balls in the tin can at first?

	Purple balls	Gold balls
Before	1x3 = 3 u	4x3 = 12 u
Change	- 3 u	- 6 u
After	0	186

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 gold balls in the end
= 12 u - 6 u
= 6 u

6 u = 186

1 u = 186 ÷ 6 = 31

Total number of balls in the tin can at first
= 3 u + 12 u
= 15 u
= 15 x 31
= 465

Answer: 465