Rael and Gabriel shared some cards in the ratio of 3 : 8. After both each gave away 63 cards to their brother, the ratio of the number of cards Rael had to the total number of cards left was 1 : 6. How many cards did the two boys have in the end?

	Rael	Gabriel	Difference
Before	3x4 = 12 u	8x4 = 32 u	5x4 = 20 u
Change	- 63	- 63
After	1x5 = 5 u	5x5 = 25 u	4x5 = 20 u

Number of cards that Rael and Gabriel each gave to their brother is the same.

The difference in the number of cards at first and in the end between Rael and Gabriel remains unchanged.  Make the difference in the number of cards the same.  LCM of 5 and 4 is 20.

Number of cards that Rael gave to their brother
= 12 u - 5 u
= 7 u

7 u = 63

1 u = 63 ÷ 7 = 9

Number of cards that the two boys had in the end
= 5 u + 25 u
= 30 u
= 30 x 9
= 270

Answer(s): 270