Cole and Ryan shared some cards in the ratio of 4 : 7. After both each gave away 50 cards to their sister, the ratio of the number of cards Cole had to the total number of cards left was 1 : 4. How many cards did the two boys have at first?

	Cole	Ryan	Difference
Before	4x2 = 8 u	7x2 = 14 u	3x2 = 6 u
Change	- 50	- 50
After	1x3 = 3 u	3x3 = 9 u	2x3 = 6 u

Number of cards that Cole and Ryan each gave to their sister is the same.

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

Number of cards that Cole gave to their sister
= 8 u - 3 u
= 5 u

5 u = 50

1 u = 50 ÷ 5 = 10

Number of cards that the two boys had at first
= 8 u + 14 u
= 22 u
= 22 x 10
= 220

Answer(s): 220