Yen had some grey stickers and black stickers in 2 packets. In Packet L, the ratio of the number of grey stickers to black stickers was 7 : 5. In Packet M, the number of grey stickers was 4 times the number of black stickers. Yen transferred ³₅ of the black stickers from Packet L to Packet M. The number of stickers in Packet L became 126 and the ratio of the number of grey stickers to black stickers in Packet M became 8 : 9.

1. How many black stickers were transferred from Packet L to Packet M?
2. What was the number of stickers in Packet M after the transfer?

	Packet L		Packet M
	Grey	Black	Grey	Black
Comparing grey stickers and black stickers at first	7 u	5 u	4x2 = 8 p	1x2 = 2 p
Before		5 u
Change		- 3 u		+ 3 u
After		2 u
Comparing grey stickers and black stickers in the end	7 u	2 u	8 p	9 p

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

9 u = 126

1 u = 126 ÷ 9 = 14

Number of black stickers that were transferred from Packet L to Packet M
= 3 u
= 3 x 14
= 42

(b)
The number of grey stickers in Packet M remains unchanged.  Make the number of grey stickers in Packet M the same.  LCM of 4 and 8 is 8. 

Increase in the number of black stickers in Packet M
= 9 p - 2 p
= 7 p

7 p = 3 u
7 p = 42

1 p = 42 ÷ 7 = 6

Number of stickers in Packet M in the end
= 8 p + 9 p
= 17 p
= 17 x 6
= 102

Answer(s): (a) 42; (b) 102