Esther had some purple pens and brown pens in 2 packets. In Packet A, the ratio of the number of purple pens to brown pens was 10 : 3. In Packet B, the number of purple pens was 2 times the number of brown pens. Esther transferred ²₃ of the brown pens from Packet A to Packet B. The number of pens in Packet A became 198 and the ratio of the number of purple pens to brown pens in Packet B became 4 : 5.

1. How many brown pens were transferred from Packet A to Packet B?
2. What was the number of pens in Packet B after the transfer?

	Packet A		Packet B
	Purple	Brown	Purple	Brown
Comparing purple pens and brown pens at first	10 u	3 u	2x2 = 4 p	1x2 = 2 p
Before		3 u
Change		- 2 u		+ 2 u
After		1 u
Comparing purple pens and brown pens in the end	10 u	1 u	4 p	5 p

(a)
Total number of pens in the end for Packet A
= 10 u + 1 u
= 11 u

11 u = 198

1 u = 198 ÷ 11 = 18

Number of brown pens that were transferred from Packet A to Packet B
= 2 u
= 2 x 18
= 36

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

Increase in the number of brown pens in Packet B
= 5 p - 2 p
= 3 p

3 p = 2 u
3 p = 36

1 p = 36 ÷ 3 = 12

Number of pens in Packet B in the end
= 4 p + 5 p
= 9 p
= 9 x 12
= 108

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