Abi had some gold marbles and blue marbles in 2 bags. In Bag F, the ratio of the number of gold marbles to blue marbles was 7 : 5. In Bag G, the number of gold marbles was 2 times the number of blue marbles. Abi transferred ²₅ of the blue marbles from Bag F to Bag G. The number of marbles in Bag F became 180 and the ratio of the number of gold marbles to blue marbles in Bag G became 4 : 5.

1. How many blue 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
	Gold	Blue	Gold	Blue
Comparing gold marbles and blue marbles at first	7 u	5 u	2x2 = 4 p	1x2 = 2 p
Before		5 u
Change		- 2 u		+ 2 u
After		3 u
Comparing gold marbles and blue marbles in the end	7 u	3 u	4 p	5 p

(a)
Total number of marbles in the end for Bag F
= 7 u + 3 u
= 10 u

10 u = 180

1 u = 180 ÷ 10 = 18

Number of blue marbles that were transferred from Bag F to Bag G
= 2 u
= 2 x 18
= 36

(b)
The number of gold marbles in Bag G remains unchanged.  Make the number of gold marbles in Bag G the same.  LCM of 2 and 4 is 4. 

Increase in the number of blue marbles in Bag G
= 5 p - 2 p
= 3 p

3 p = 2 u
3 p = 36

1 p = 36 ÷ 3 = 12

Number of marbles in Bag G in the end
= 4 p + 5 p
= 9 p
= 9 x 12
= 108

Answer(s): (a) 36; (b) 108