Xandra had some purple stamps and black stamps in 2 packets. In Packet N, the ratio of the number of purple stamps to black stamps was 7 : 3. In Packet P, the number of purple stamps was 2 times the number of black stamps. Xandra transferred ²₃ of the black stamps from Packet N to Packet P. The number of stamps in Packet N became 80 and the ratio of the number of purple stamps to black stamps in Packet P became 6 : 7.

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

	Packet N		Packet P
	Purple	Black	Purple	Black
Comparing purple stamps and black stamps at first	7 u	3 u	2x3 = 6 p	1x3 = 3 p
Before		3 u
Change		- 2 u		+ 2 u
After		1 u
Comparing purple stamps and black stamps in the end	7 u	1 u	6 p	7 p

(a)
Total number of stamps in the end for Packet N
= 7 u + 1 u
= 8 u

8 u = 80

1 u = 80 ÷ 8 = 10

Number of black stamps that were transferred from Packet N to Packet P
= 2 u
= 2 x 10
= 20

(b)
The number of purple stamps in Packet P remains unchanged.  Make the number of purple stamps in Packet P the same.  LCM of 2 and 6 is 6. 

Increase in the number of black stamps in Packet P
= 7 p - 3 p
= 4 p

4 p = 2 u
4 p = 20

1 p = 20 ÷ 4 = 5

Number of stamps in Packet P in the end
= 6 p + 7 p
= 13 p
= 13 x 5
= 65

Answer(s): (a) 20; (b) 65