Tina had some gold pens and grey pens in 2 boxes. In Box S, the ratio of the number of gold pens to grey pens was 7 : 3. In Box T, the number of gold pens was 2 times the number of grey pens. Tina transferred ²₃ of the grey pens from Box S to Box T. The number of pens in Box S became 96 and the ratio of the number of gold pens to grey pens in Box T became 4 : 5.

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

	Box S		Box T
	Gold	Grey	Gold	Grey
Comparing gold pens and grey pens at first	7 u	3 u	2x2 = 4 p	1x2 = 2 p
Before		3 u
Change		- 2 u		+ 2 u
After		1 u
Comparing gold pens and grey pens in the end	7 u	1 u	4 p	5 p

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

8 u = 96

1 u = 96 ÷ 8 = 12

Number of grey pens that were transferred from Box S to Box T
= 2 u
= 2 x 12
= 24

(b)
The number of gold pens in Box T remains unchanged.  Make the number of gold pens in Box T the same.  LCM of 2 and 4 is 4. 

Increase in the number of grey pens in Box T
= 5 p - 2 p
= 3 p

3 p = 2 u
3 p = 24

1 p = 24 ÷ 3 = 8

Number of pens in Box T in the end
= 4 p + 5 p
= 9 p
= 9 x 8
= 72

Answer(s): (a) 24; (b) 72