In a tin can, the ratio of the number of brown balls to the number of purple balls was 1 : 4. Each time, 3 brown and 7 purple balls were taken out of the tin can. A while later, only 120 purple balls were left in the tin can. What was the total number of balls in the tin can at first?

	Brown balls	Purple balls
Before	1x3 = 3 u	4x3 = 12 u
Change	- 3 u	- 7 u
After	0	120

Since there is no brown balls left, this means that the number of brown marbles at first is the same as the number of brown marbles taken out.  

Make the number of brown balls at first and taken out the same.  LCM of 1 and 3 is 3.

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

5 u = 120

1 u = 120 ÷ 5 = 24

Total number of balls in the tin can at first
= 3 u + 12 u
= 15 u
= 15 x 24
= 360

Answer: 360