Sean and Pierre shared some cards in the ratio of 5 : 8. After both each gave away 70 cards to their brother, the ratio of the number of cards Sean had to the total number of cards left was 1 : 4. How many cards did the two boys have in the end?

	Sean	Pierre	Difference
Before	5x2 = 10 u	8x2 = 16 u	3x2 = 6 u
Change	- 70	- 70
After	1x3 = 3 u	3x3 = 9 u	2x3 = 6 u

Number of cards that Sean and Pierre each gave to their brother is the same.

The difference in the number of cards at first and in the end between Sean and Pierre remains unchanged.  Make the difference in the number of cards the same.  LCM of 3 and 2 is 6.

Number of cards that Sean gave to their brother
= 10 u - 3 u
= 7 u

7 u = 70

1 u = 70 ÷ 7 = 10

Number of cards that the two boys had in the end
= 3 u + 9 u
= 12 u
= 12 x 10
= 120

Answer(s): 120