Ethan and Cole shared some cards in the ratio of 5 : 8. After both each gave away 187 cards to their sister, the ratio of the number of cards Ethan had to the total number of cards left was 1 : 6. How many cards did the two boys have at first?

	Ethan	Cole	Difference
Before	5x4 = 20 u	8x4 = 32 u	3x4 = 12 u
Change	- 187	- 187
After	1x3 = 3 u	5x3 = 15 u	4x3 = 12 u

Number of cards that Ethan and Cole each gave to their sister is the same.

The difference in the number of cards at first and in the end between Ethan and Cole remains unchanged.  Make the difference in the number of cards the same.  LCM of 3 and 4 is 12.

Number of cards that Ethan gave to their sister
= 20 u - 3 u
= 17 u

17 u = 187

1 u = 187 ÷ 17 = 11

Number of cards that the two boys had at first
= 20 u + 32 u
= 52 u
= 52 x 11
= 572

Answer(s): 572