Emily had some blue pens and grey pens in 2 packets. In Packet H, the ratio of the number of blue pens to grey pens was 7 : 5. In Packet J, the number of blue pens was 4 times the number of grey pens. Emily transferred ³₅ of the grey pens from Packet H to Packet J. The number of pens in Packet H became 63 and the ratio of the number of blue pens to grey pens in Packet J became 8 : 9.

1. How many grey pens were transferred from Packet H to Packet J?
2. What was the number of pens in Packet J after the transfer?

	Packet H		Packet J
	Blue	Grey	Blue	Grey
Comparing blue pens and grey pens at first	7 u	5 u	4x2 = 8 p	1x2 = 2 p
Before		5 u
Change		- 3 u		+ 3 u
After		2 u
Comparing blue pens and grey pens in the end	7 u	2 u	8 p	9 p

(a)
Total number of pens in the end for Packet H
= 7 u + 2 u
= 9 u

9 u = 63

1 u = 63 ÷ 9 = 7

Number of grey pens that were transferred from Packet H to Packet J
= 3 u
= 3 x 7
= 21

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

Increase in the number of grey pens in Packet J
= 9 p - 2 p
= 7 p

7 p = 3 u
7 p = 21

1 p = 21 ÷ 7 = 3

Number of pens in Packet J in the end
= 8 p + 9 p
= 17 p
= 17 x 3
= 51

Answer(s): (a) 21; (b) 51