Ivan and Justin shared some cards in the ratio of 5 : 7. After both each gave away 27 cards to their brother, the ratio of the number of cards Ivan had to the total number of cards left was 1 : 6. How many cards did the two boys have in the end?

	Ivan	Justin	Difference
Before	5x2 = 10 u	7x2 = 14 u	2x2 = 4 u
Change	- 27	- 27
After	1x1 = 1 u	5x1 = 5 u	4x1 = 4 u

Number of cards that Ivan and Justin each gave to their brother is the same.

The difference in the number of cards at first and in the end between Ivan and Justin remains unchanged.  Make the difference in the number of cards the same.  LCM of 2 and 4 is 4.

Number of cards that Ivan gave to their brother
= 10 u - 1 u
= 9 u

9 u = 27

1 u = 27 ÷ 9 = 3

Number of cards that the two boys had in the end
= 1 u + 5 u
= 6 u
= 6 x 3
= 18

Answer(s): 18