Reggie and Vincent shared some cards in the ratio of 5 : 7. After both each gave away 24 cards to their cousin, the ratio of the number of cards Reggie had to the total number of cards left was 1 : 3. How many cards did the two boys have in the end?

	Reggie	Vincent	Difference
Before	5x1 = 5 u	7x1 = 7 u	2x1 = 2 u
Change	- 24	- 24
After	1x2 = 2 u	2x2 = 4 u	1x2 = 2 u

Number of cards that Reggie and Vincent each gave to their cousin is the same.

The difference in the number of cards at first and in the end between Reggie and Vincent remains unchanged.  Make the difference in the number of cards the same.  LCM of 2 and 1 is 2.

Number of cards that Reggie gave to their cousin
= 5 u - 2 u
= 3 u

3 u = 24

1 u = 24 ÷ 3 = 8

Number of cards that the two boys had in the end
= 2 u + 4 u
= 6 u
= 6 x 8
= 48

Answer(s): 48