In a bag, the ratio of the number of grey marbles to the number of purple marbles was 1 : 3. Each time, 4 grey and 7 purple marbles were taken out of the bag. A while later, only 85 purple marbles were left in the bag. What was the total number of marbles in the bag at first?

	Grey marbles	Purple marbles
Before	1x4 = 4 u	3x4 = 12 u
Change	- 4 u	- 7 u
After	0	85

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

Make the number of grey marbles at first and taken out the same.  LCM of 1 and 4 is 4.

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

5 u = 85

1 u = 85 ÷ 5 = 17

Total number of marbles in the bag at first
= 4 u + 12 u
= 16 u
= 16 x 17
= 272

Answer: 272