Natalie had some white pens and silver pens in 2 boxes. In Box X, the ratio of the number of white pens to silver pens was 7 : 3. In Box Y, the number of white pens was 2 times the number of silver pens. Natalie transferred ²₃ of the silver pens from Box X to Box Y. The number of pens in Box X became 32 and the ratio of the number of white pens to silver pens in Box Y became 6 : 7.

1. How many silver pens were transferred from Box X to Box Y?
2. What was the number of pens in Box Y after the transfer?

	Box X		Box Y
	White	Silver	White	Silver
Comparing white pens and silver pens at first	7 u	3 u	2x3 = 6 p	1x3 = 3 p
Before		3 u
Change		- 2 u		+ 2 u
After		1 u
Comparing white pens and silver pens in the end	7 u	1 u	6 p	7 p

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

8 u = 32

1 u = 32 ÷ 8 = 4

Number of silver pens that were transferred from Box X to Box Y
= 2 u
= 2 x 4
= 8

(b)
The number of white pens in Box Y remains unchanged.  Make the number of white pens in Box Y the same.  LCM of 2 and 6 is 6. 

Increase in the number of silver pens in Box Y
= 7 p - 3 p
= 4 p

4 p = 2 u
4 p = 8

1 p = 8 ÷ 4 = 2

Number of pens in Box Y in the end
= 6 p + 7 p
= 13 p
= 13 x 2
= 26

Answer(s): (a) 8; (b) 26