Elyse had some pink erasers and green erasers in 2 bags. In Bag J, the ratio of the number of pink erasers to green erasers was 9 : 5. In Bag K, the number of pink erasers was 2 times the number of green erasers. Elyse transferred ²₅ of the green erasers from Bag J to Bag K. The number of erasers in Bag J became 108 and the ratio of the number of pink erasers to green erasers in Bag K became 4 : 5.

1. How many green erasers were transferred from Bag J to Bag K?
2. What was the number of erasers in Bag K after the transfer?

	Bag J		Bag K
	Pink	Green	Pink	Green
Comparing pink erasers and green erasers at first	9 u	5 u	2x2 = 4 p	1x2 = 2 p
Before		5 u
Change		- 2 u		+ 2 u
After		3 u
Comparing pink erasers and green erasers in the end	9 u	3 u	4 p	5 p

(a)
Total number of erasers in the end for Bag J
= 9 u + 3 u
= 12 u

12 u = 108

1 u = 108 ÷ 12 = 9

Number of green erasers that were transferred from Bag J to Bag K
= 2 u
= 2 x 9
= 18

(b)
The number of pink erasers in Bag K remains unchanged.  Make the number of pink erasers in Bag K the same.  LCM of 2 and 4 is 4. 

Increase in the number of green erasers in Bag K
= 5 p - 2 p
= 3 p

3 p = 2 u
3 p = 18

1 p = 18 ÷ 3 = 6

Number of erasers in Bag K in the end
= 4 p + 5 p
= 9 p
= 9 x 6
= 54

Answer(s): (a) 18; (b) 54