Pamela had some white pens and brown pens in 2 boxes. In Box K, the ratio of the number of white pens to brown pens was 9 : 7. In Box L, the number of white pens was 2 times the number of brown pens. Pamela transferred ²₇ of the brown pens from Box K to Box L. The number of pens in Box K became 126 and the ratio of the number of white pens to brown pens in Box L became 4 : 5.

1. How many brown pens were transferred from Box K to Box L?
2. What was the number of pens in Box L after the transfer?

	Box K		Box L
	White	Brown	White	Brown
Comparing white pens and brown pens at first	9 u	7 u	2x2 = 4 p	1x2 = 2 p
Before		7 u
Change		- 2 u		+ 2 u
After		5 u
Comparing white pens and brown pens in the end	9 u	5 u	4 p	5 p

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

14 u = 126

1 u = 126 ÷ 14 = 9

Number of brown pens that were transferred from Box K to Box L
= 2 u
= 2 x 9
= 18

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

Increase in the number of brown pens in Box L
= 5 p - 2 p
= 3 p

3 p = 2 u
3 p = 18

1 p = 18 ÷ 3 = 6

Number of pens in Box L in the end
= 4 p + 5 p
= 9 p
= 9 x 6
= 54

Answer(s): (a) 18; (b) 54