Cindy had some purple beads and blue beads in 2 bags. In Bag X, the ratio of the number of purple beads to blue beads was 10 : 3. In Bag Y, the number of purple beads was 2 times the number of blue beads. Cindy transferred ²₃ of the blue beads from Bag X to Bag Y. The number of beads in Bag X became 66 and the ratio of the number of purple beads to blue beads in Bag Y became 4 : 5.

1. How many blue beads were transferred from Bag X to Bag Y?
2. What was the number of beads in Bag Y after the transfer?

	Bag X		Bag Y
	Purple	Blue	Purple	Blue
Comparing purple beads and blue beads at first	10 u	3 u	2x2 = 4 p	1x2 = 2 p
Before		3 u
Change		- 2 u		+ 2 u
After		1 u
Comparing purple beads and blue beads in the end	10 u	1 u	4 p	5 p

(a)
Total number of beads in the end for Bag X
= 10 u + 1 u
= 11 u

11 u = 66

1 u = 66 ÷ 11 = 6

Number of blue beads that were transferred from Bag X to Bag Y
= 2 u
= 2 x 6
= 12

(b)
The number of purple beads in Bag Y remains unchanged.  Make the number of purple beads in Bag Y the same.  LCM of 2 and 4 is 4. 

Increase in the number of blue beads in Bag Y
= 5 p - 2 p
= 3 p

3 p = 2 u
3 p = 12

1 p = 12 ÷ 3 = 4

Number of beads in Bag Y in the end
= 4 p + 5 p
= 9 p
= 9 x 4
= 36

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