Jen had some purple pens and green pens in 2 bags. In Bag N, the ratio of the number of purple pens to green pens was 9 : 7. In Bag P, the number of purple pens was 2 times the number of green pens. Jen transferred ²₇ of the green pens from Bag N to Bag P. The number of pens in Bag N became 252 and the ratio of the number of purple pens to green pens in Bag P became 4 : 5.

1. How many green pens were transferred from Bag N to Bag P?
2. What was the number of pens in Bag P after the transfer?

	Bag N		Bag P
	Purple	Green	Purple	Green
Comparing purple pens and green pens at first	9 u	7 u	2x2 = 4 p	1x2 = 2 p
Before		7 u
Change		- 2 u		+ 2 u
After		5 u
Comparing purple pens and green pens in the end	9 u	5 u	4 p	5 p

(a)
Total number of pens in the end for Bag N
= 9 u + 5 u
= 14 u

14 u = 252

1 u = 252 ÷ 14 = 18

Number of green pens that were transferred from Bag N to Bag P
= 2 u
= 2 x 18
= 36

(b)
The number of purple pens in Bag P remains unchanged.  Make the number of purple pens in Bag P the same.  LCM of 2 and 4 is 4. 

Increase in the number of green pens in Bag P
= 5 p - 2 p
= 3 p

3 p = 2 u
3 p = 36

1 p = 36 ÷ 3 = 12

Number of pens in Bag P in the end
= 4 p + 5 p
= 9 p
= 9 x 12
= 108

Answer(s): (a) 36; (b) 108