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

	Oscar	Ethan	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 Oscar and Ethan each gave to their brother is the same.

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

Number of cards that Oscar gave to their brother
= 20 u - 3 u
= 17 u

17 u = 187

1 u = 187 ÷ 17 = 11

Number of cards that the two boys had in the end
= 3 u + 15 u
= 18 u
= 18 x 11
= 198

Answer(s): 198