Xandra had some silver stamps and black stamps in 2 packets. In Packet Y, the ratio of the number of silver stamps to black stamps was 9 : 7. In Packet Z, the number of silver stamps was 3 times the number of black stamps. Xandra transferred ³₇ of the black stamps from Packet Y to Packet Z. The number of stamps in Packet Y became 260 and the ratio of the number of silver stamps to black stamps in Packet Z became 6 : 7.

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

	Packet Y		Packet Z
	Silver	Black	Silver	Black
Comparing silver stamps and black stamps at first	9 u	7 u	3x2 = 6 p	1x2 = 2 p
Before		7 u
Change		- 3 u		+ 3 u
After		4 u
Comparing silver stamps and black stamps in the end	9 u	4 u	6 p	7 p

(a)
Total number of stamps in the end for Packet Y
= 9 u + 4 u
= 13 u

13 u = 260

1 u = 260 ÷ 13 = 20

Number of black stamps that were transferred from Packet Y to Packet Z
= 3 u
= 3 x 20
= 60

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

Increase in the number of black stamps in Packet Z
= 7 p - 2 p
= 5 p

5 p = 3 u
5 p = 60

1 p = 60 ÷ 5 = 12

Number of stamps in Packet Z in the end
= 6 p + 7 p
= 13 p
= 13 x 12
= 156

Answer(s): (a) 60; (b) 156