Hilda had some yellow pens and pink pens in 2 packets. In Packet Q, the ratio of the number of yellow pens to pink pens was 7 : 3. In Packet R, the number of yellow pens was 3 times the number of pink pens. Hilda transferred ²₃ of the pink pens from Packet Q to Packet R. The number of pens in Packet Q became 120 and the ratio of the number of yellow pens to pink pens in Packet R became 6 : 7.

1. How many pink pens were transferred from Packet Q to Packet R?
2. What was the number of pens in Packet R after the transfer?

	Packet Q		Packet R
	Yellow	Pink	Yellow	Pink
Comparing yellow pens and pink pens at first	7 u	3 u	3x2 = 6 p	1x2 = 2 p
Before		3 u
Change		- 2 u		+ 2 u
After		1 u
Comparing yellow pens and pink pens in the end	7 u	1 u	6 p	7 p

(a)
Total number of pens in the end for Packet Q
= 7 u + 1 u
= 8 u

8 u = 120

1 u = 120 ÷ 8 = 15

Number of pink pens that were transferred from Packet Q to Packet R
= 2 u
= 2 x 15
= 30

(b)
The number of yellow pens in Packet R remains unchanged.  Make the number of yellow pens in Packet R the same.  LCM of 3 and 6 is 6. 

Increase in the number of pink pens in Packet R
= 7 p - 2 p
= 5 p

5 p = 2 u
5 p = 30

1 p = 30 ÷ 5 = 6

Number of pens in Packet R in the end
= 6 p + 7 p
= 13 p
= 13 x 6
= 78

Answer(s): (a) 30; (b) 78