Nora had some silver cards and green cards in 2 bags. In Bag R, the ratio of the number of silver cards to green cards was 7 : 3. In Bag S, the number of silver cards was 2 times the number of green cards. Nora transferred ²₃ of the green cards from Bag R to Bag S. The number of cards in Bag R became 48 and the ratio of the number of silver cards to green cards in Bag S became 4 : 5.

1. How many green cards were transferred from Bag R to Bag S?
2. What was the number of cards in Bag S after the transfer?

	Bag R		Bag S
	Silver	Green	Silver	Green
Comparing silver cards and green cards at first	7 u	3 u	2x2 = 4 p	1x2 = 2 p
Before		3 u
Change		- 2 u		+ 2 u
After		1 u
Comparing silver cards and green cards in the end	7 u	1 u	4 p	5 p

(a)
Total number of cards in the end for Bag R
= 7 u + 1 u
= 8 u

8 u = 48

1 u = 48 ÷ 8 = 6

Number of green cards that were transferred from Bag R to Bag S
= 2 u
= 2 x 6
= 12

(b)
The number of silver cards in Bag S remains unchanged.  Make the number of silver cards in Bag S the same.  LCM of 2 and 4 is 4. 

Increase in the number of green cards in Bag S
= 5 p - 2 p
= 3 p

3 p = 2 u
3 p = 12

1 p = 12 ÷ 3 = 4

Number of cards in Bag S in the end
= 4 p + 5 p
= 9 p
= 9 x 4
= 36

Answer(s): (a) 12; (b) 36