Tiffany had some yellow stickers and purple stickers in 2 packets. In Packet F, the ratio of the number of yellow stickers to purple stickers was 8 : 5. In Packet G, the number of yellow stickers was 2 times the number of purple stickers. Tiffany transferred ³₅ of the purple stickers from Packet F to Packet G. The number of stickers in Packet F became 80 and the ratio of the number of yellow stickers to purple stickers in Packet G became 6 : 7.

1. How many purple stickers were transferred from Packet F to Packet G?
2. What was the number of stickers in Packet G after the transfer?

	Packet F		Packet G
	Yellow	Purple	Yellow	Purple
Comparing yellow stickers and purple stickers at first	8 u	5 u	2x3 = 6 p	1x3 = 3 p
Before		5 u
Change		- 3 u		+ 3 u
After		2 u
Comparing yellow stickers and purple stickers in the end	8 u	2 u	6 p	7 p

(a)
Total number of stickers in the end for Packet F
= 8 u + 2 u
= 10 u

10 u = 80

1 u = 80 ÷ 10 = 8

Number of purple stickers that were transferred from Packet F to Packet G
= 3 u
= 3 x 8
= 24

(b)
The number of yellow stickers in Packet G remains unchanged.  Make the number of yellow stickers in Packet G the same.  LCM of 2 and 6 is 6. 

Increase in the number of purple stickers in Packet G
= 7 p - 3 p
= 4 p

4 p = 3 u
4 p = 24

1 p = 24 ÷ 4 = 6

Number of stickers in Packet G in the end
= 6 p + 7 p
= 13 p
= 13 x 6
= 78

Answer(s): (a) 24; (b) 78