Ken and Nick shared some cards in the ratio of 5 : 8. After both each gave away 153 cards to their brother, the ratio of the number of cards Ken had to the total number of cards left was 1 : 6. How many cards did the two boys have in the end?

	Ken	Nick	Difference
Before	5x4 = 20 u	8x4 = 32 u	3x4 = 12 u
Change	- 153	- 153
After	1x3 = 3 u	5x3 = 15 u	4x3 = 12 u

Number of cards that Ken and Nick each gave to their brother is the same.

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

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

17 u = 153

1 u = 153 ÷ 17 = 9

Number of cards that the two boys had in the end
= 3 u + 15 u
= 18 u
= 18 x 9
= 162

Answer(s): 162