Xylia had some yellow pens and silver pens in 2 packets. In Packet P, the ratio of the number of yellow pens to silver pens was 8 : 7. In Packet Q, the number of yellow pens was 2 times the number of silver pens. Xylia transferred ²₇ of the silver pens from Packet P to Packet Q. The number of pens in Packet P became 234 and the ratio of the number of yellow pens to silver pens in Packet Q became 4 : 5.

1. How many silver pens were transferred from Packet P to Packet Q?
2. What was the number of pens in Packet Q after the transfer?

	Packet P		Packet Q
	Yellow	Silver	Yellow	Silver
Comparing yellow pens and silver pens at first	8 u	7 u	2x2 = 4 p	1x2 = 2 p
Before		7 u
Change		- 2 u		+ 2 u
After		5 u
Comparing yellow pens and silver pens in the end	8 u	5 u	4 p	5 p

(a)
Total number of pens in the end for Packet P
= 8 u + 5 u
= 13 u

13 u = 234

1 u = 234 ÷ 13 = 18

Number of silver pens that were transferred from Packet P to Packet Q
= 2 u
= 2 x 18
= 36

(b)
The number of yellow pens in Packet Q remains unchanged.  Make the number of yellow pens in Packet Q the same.  LCM of 2 and 4 is 4. 

Increase in the number of silver pens in Packet Q
= 5 p - 2 p
= 3 p

3 p = 2 u
3 p = 36

1 p = 36 ÷ 3 = 12

Number of pens in Packet Q in the end
= 4 p + 5 p
= 9 p
= 9 x 12
= 108

Answer(s): (a) 36; (b) 108