Xuan had some silver beads and blue beads in 2 packets. In Packet X, the ratio of the number of silver beads to blue beads was 8 : 5. In Packet Y, the number of silver beads was 2 times the number of blue beads. Xuan transferred ³₅ of the blue beads from Packet X to Packet Y. The number of beads in Packet X became 80 and the ratio of the number of silver beads to blue beads in Packet Y became 6 : 7.

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

	Packet X		Packet Y
	Silver	Blue	Silver	Blue
Comparing silver beads and blue beads at first	8 u	5 u	2x3 = 6 p	1x3 = 3 p
Before		5 u
Change		- 3 u		+ 3 u
After		2 u
Comparing silver beads and blue beads in the end	8 u	2 u	6 p	7 p

(a)
Total number of beads in the end for Packet X
= 8 u + 2 u
= 10 u

10 u = 80

1 u = 80 ÷ 10 = 8

Number of blue beads that were transferred from Packet X to Packet Y
= 3 u
= 3 x 8
= 24

(b)
The number of silver beads in Packet Y remains unchanged.  Make the number of silver beads in Packet Y the same.  LCM of 2 and 6 is 6. 

Increase in the number of blue beads in Packet Y
= 7 p - 3 p
= 4 p

4 p = 3 u
4 p = 24

1 p = 24 ÷ 4 = 6

Number of beads in Packet Y in the end
= 6 p + 7 p
= 13 p
= 13 x 6
= 78

Answer(s): (a) 24; (b) 78