Gem had some white pens and pink pens in 2 bags. In Bag J, the ratio of the number of white pens to pink pens was 10 : 7. In Bag K, the number of white pens was 2 times the number of pink pens. Gem transferred ²₇ of the pink pens from Bag J to Bag K. The number of pens in Bag J became 300 and the ratio of the number of white pens to pink pens in Bag K became 6 : 7.

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

	Bag J		Bag K
	White	Pink	White	Pink
Comparing white pens and pink pens at first	10 u	7 u	2x3 = 6 p	1x3 = 3 p
Before		7 u
Change		- 2 u		+ 2 u
After		5 u
Comparing white pens and pink pens in the end	10 u	5 u	6 p	7 p

(a)
Total number of pens in the end for Bag J
= 10 u + 5 u
= 15 u

15 u = 300

1 u = 300 ÷ 15 = 20

Number of pink pens that were transferred from Bag J to Bag K
= 2 u
= 2 x 20
= 40

(b)
The number of white pens in Bag K remains unchanged.  Make the number of white pens in Bag K the same.  LCM of 2 and 6 is 6. 

Increase in the number of pink pens in Bag K
= 7 p - 3 p
= 4 p

4 p = 2 u
4 p = 40

1 p = 40 ÷ 4 = 10

Number of pens in Bag K in the end
= 6 p + 7 p
= 13 p
= 13 x 10
= 130

Answer(s): (a) 40; (b) 130