Erika had some silver beads and blue beads in 2 packets. In Packet H, the ratio of the number of silver beads to blue beads was 9 : 5. In Packet J, the number of silver beads was 3 times the number of blue beads. Erika transferred ⁴₅ of the blue beads from Packet H to Packet J. The number of beads in Packet H became 200 and the ratio of the number of silver beads to blue beads in Packet J became 6 : 7.

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

	Packet H		Packet J
	Silver	Blue	Silver	Blue
Comparing silver beads and blue beads at first	9 u	5 u	3x2 = 6 p	1x2 = 2 p
Before		5 u
Change		- 4 u		+ 4 u
After		1 u
Comparing silver beads and blue beads in the end	9 u	1 u	6 p	7 p

(a)
Total number of beads in the end for Packet H
= 9 u + 1 u
= 10 u

10 u = 200

1 u = 200 ÷ 10 = 20

Number of blue beads that were transferred from Packet H to Packet J
= 4 u
= 4 x 20
= 80

(b)
The number of silver beads in Packet J remains unchanged.  Make the number of silver beads in Packet J the same.  LCM of 3 and 6 is 6. 

Increase in the number of blue beads in Packet J
= 7 p - 2 p
= 5 p

5 p = 4 u
5 p = 80

1 p = 80 ÷ 5 = 16

Number of beads in Packet J in the end
= 6 p + 7 p
= 13 p
= 13 x 16
= 208

Answer(s): (a) 80; (b) 208