Raeann had some yellow pens and silver pens in 2 packets. In Packet D, the ratio of the number of yellow pens to silver pens was 9 : 7. In Packet E, the number of yellow pens was 4 times the number of silver pens. Raeann transferred ⁴₇ of the silver pens from Packet D to Packet E. The number of pens in Packet D became 168 and the ratio of the number of yellow pens to silver pens in Packet E became 8 : 9.

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

	Packet D		Packet E
	Yellow	Silver	Yellow	Silver
Comparing yellow pens and silver pens at first	9 u	7 u	4x2 = 8 p	1x2 = 2 p
Before		7 u
Change		- 4 u		+ 4 u
After		3 u
Comparing yellow pens and silver pens in the end	9 u	3 u	8 p	9 p

(a)
Total number of pens in the end for Packet D
= 9 u + 3 u
= 12 u

12 u = 168

1 u = 168 ÷ 12 = 14

Number of silver pens that were transferred from Packet D to Packet E
= 4 u
= 4 x 14
= 56

(b)
The number of yellow pens in Packet E remains unchanged.  Make the number of yellow pens in Packet E the same.  LCM of 4 and 8 is 8. 

Increase in the number of silver pens in Packet E
= 9 p - 2 p
= 7 p

7 p = 4 u
7 p = 56

1 p = 56 ÷ 7 = 8

Number of pens in Packet E in the end
= 8 p + 9 p
= 17 p
= 17 x 8
= 136

Answer(s): (a) 56; (b) 136