Vanessa had some silver pens and grey pens in 2 bags. In Bag S, the ratio of the number of silver pens to grey pens was 9 : 7. In Bag T, the number of silver pens was 3 times the number of grey pens. Vanessa transferred ²₇ of the grey pens from Bag S to Bag T. The number of pens in Bag S became 140 and the ratio of the number of silver pens to grey pens in Bag T became 6 : 7.

1. How many grey pens were transferred from Bag S to Bag T?
2. What was the number of pens in Bag T after the transfer?

	Bag S		Bag T
	Silver	Grey	Silver	Grey
Comparing silver pens and grey pens at first	9 u	7 u	3x2 = 6 p	1x2 = 2 p
Before		7 u
Change		- 2 u		+ 2 u
After		5 u
Comparing silver pens and grey pens in the end	9 u	5 u	6 p	7 p

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

14 u = 140

1 u = 140 ÷ 14 = 10

Number of grey pens that were transferred from Bag S to Bag T
= 2 u
= 2 x 10
= 20

(b)
The number of silver pens in Bag T remains unchanged.  Make the number of silver pens in Bag T the same.  LCM of 3 and 6 is 6. 

Increase in the number of grey pens in Bag T
= 7 p - 2 p
= 5 p

5 p = 2 u
5 p = 20

1 p = 20 ÷ 5 = 4

Number of pens in Bag T in the end
= 6 p + 7 p
= 13 p
= 13 x 4
= 52

Answer(s): (a) 20; (b) 52