Xuan had some red stickers and purple stickers in 2 bags. In Bag E, the ratio of the number of red stickers to purple stickers was 10 : 3. In Bag F, the number of red stickers was 2 times the number of purple stickers. Xuan transferred ²₃ of the purple stickers from Bag E to Bag F. The number of stickers in Bag E became 165 and the ratio of the number of red stickers to purple stickers in Bag F became 4 : 5.

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

	Bag E		Bag F
	Red	Purple	Red	Purple
Comparing red stickers and purple stickers at first	10 u	3 u	2x2 = 4 p	1x2 = 2 p
Before		3 u
Change		- 2 u		+ 2 u
After		1 u
Comparing red stickers and purple stickers in the end	10 u	1 u	4 p	5 p

(a)
Total number of stickers in the end for Bag E
= 10 u + 1 u
= 11 u

11 u = 165

1 u = 165 ÷ 11 = 15

Number of purple stickers that were transferred from Bag E to Bag F
= 2 u
= 2 x 15
= 30

(b)
The number of red stickers in Bag F remains unchanged.  Make the number of red stickers in Bag F the same.  LCM of 2 and 4 is 4. 

Increase in the number of purple stickers in Bag F
= 5 p - 2 p
= 3 p

3 p = 2 u
3 p = 30

1 p = 30 ÷ 3 = 10

Number of stickers in Bag F in the end
= 4 p + 5 p
= 9 p
= 9 x 10
= 90

Answer(s): (a) 30; (b) 90