Zoe had some silver marbles and purple marbles in 2 bags. In Bag W, the ratio of the number of silver marbles to purple marbles was 9 : 5. In Bag X, the number of silver marbles was 2 times the number of purple marbles. Zoe transferred ²₅ of the purple marbles from Bag W to Bag X. The number of marbles in Bag W became 216 and the ratio of the number of silver marbles to purple marbles in Bag X became 4 : 5.

1. How many purple marbles were transferred from Bag W to Bag X?
2. What was the number of marbles in Bag X after the transfer?

	Bag W		Bag X
	Silver	Purple	Silver	Purple
Comparing silver marbles and purple marbles at first	9 u	5 u	2x2 = 4 p	1x2 = 2 p
Before		5 u
Change		- 2 u		+ 2 u
After		3 u
Comparing silver marbles and purple marbles in the end	9 u	3 u	4 p	5 p

(a)
Total number of marbles in the end for Bag W
= 9 u + 3 u
= 12 u

12 u = 216

1 u = 216 ÷ 12 = 18

Number of purple marbles that were transferred from Bag W to Bag X
= 2 u
= 2 x 18
= 36

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

Increase in the number of purple marbles in Bag X
= 5 p - 2 p
= 3 p

3 p = 2 u
3 p = 36

1 p = 36 ÷ 3 = 12

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

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