Emily had some silver stamps and black stamps in 2 packets. In Packet X, the ratio of the number of silver stamps to black stamps was 8 : 5. In Packet Y, the number of silver stamps was 4 times the number of black stamps. Emily transferred ²₅ of the black stamps from Packet X to Packet Y. The number of stamps in Packet X became 77 and the ratio of the number of silver stamps to black stamps in Packet Y became 8 : 9.

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

	Packet X		Packet Y
	Silver	Black	Silver	Black
Comparing silver stamps and black stamps at first	8 u	5 u	4x2 = 8 p	1x2 = 2 p
Before		5 u
Change		- 2 u		+ 2 u
After		3 u
Comparing silver stamps and black stamps in the end	8 u	3 u	8 p	9 p

(a)
Total number of stamps in the end for Packet X
= 8 u + 3 u
= 11 u

11 u = 77

1 u = 77 ÷ 11 = 7

Number of black stamps that were transferred from Packet X to Packet Y
= 2 u
= 2 x 7
= 14

(b)
The number of silver stamps in Packet Y remains unchanged.  Make the number of silver stamps in Packet Y the same.  LCM of 4 and 8 is 8. 

Increase in the number of black stamps in Packet Y
= 9 p - 2 p
= 7 p

7 p = 2 u
7 p = 14

1 p = 14 ÷ 7 = 2

Number of stamps in Packet Y in the end
= 8 p + 9 p
= 17 p
= 17 x 2
= 34

Answer(s): (a) 14; (b) 34