Shannon had some grey marbles and green marbles in 2 bags. In Bag F, the ratio of the number of grey marbles to green marbles was 8 : 5. In Bag G, the number of grey marbles was 2 times the number of green marbles. Shannon transferred ²₅ of the green marbles from Bag F to Bag G. The number of marbles in Bag F became 44 and the ratio of the number of grey marbles to green marbles in Bag G became 6 : 7.

1. How many green marbles were transferred from Bag F to Bag G?
2. What was the number of marbles in Bag G after the transfer?

	Bag F		Bag G
	Grey	Green	Grey	Green
Comparing grey marbles and green marbles at first	8 u	5 u	2x3 = 6 p	1x3 = 3 p
Before		5 u
Change		- 2 u		+ 2 u
After		3 u
Comparing grey marbles and green marbles in the end	8 u	3 u	6 p	7 p

(a)
Total number of marbles in the end for Bag F
= 8 u + 3 u
= 11 u

11 u = 44

1 u = 44 ÷ 11 = 4

Number of green marbles that were transferred from Bag F to Bag G
= 2 u
= 2 x 4
= 8

(b)
The number of grey marbles in Bag G remains unchanged.  Make the number of grey marbles in Bag G the same.  LCM of 2 and 6 is 6. 

Increase in the number of green marbles in Bag G
= 7 p - 3 p
= 4 p

4 p = 2 u
4 p = 8

1 p = 8 ÷ 4 = 2

Number of marbles in Bag G in the end
= 6 p + 7 p
= 13 p
= 13 x 2
= 26

Answer(s): (a) 8; (b) 26