Cindy had some white pens and grey pens in 2 boxes. In Box U, the ratio of the number of white pens to grey pens was 9 : 5. In Box V, the number of white pens was 5 times the number of grey pens. Cindy transferred ⁴₅ of the grey pens from Box U to Box V. The number of pens in Box U became 90 and the ratio of the number of white pens to grey pens in Box V became 10 : 11.

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

	Box U		Box V
	White	Grey	White	Grey
Comparing white pens and grey pens at first	9 u	5 u	5x2 = 10 p	1x2 = 2 p
Before		5 u
Change		- 4 u		+ 4 u
After		1 u
Comparing white pens and grey pens in the end	9 u	1 u	10 p	11 p

(a)
Total number of pens in the end for Box U
= 9 u + 1 u
= 10 u

10 u = 90

1 u = 90 ÷ 10 = 9

Number of grey pens that were transferred from Box U to Box V
= 4 u
= 4 x 9
= 36

(b)
The number of white pens in Box V remains unchanged.  Make the number of white pens in Box V the same.  LCM of 5 and 10 is 10. 

Increase in the number of grey pens in Box V
= 11 p - 2 p
= 9 p

9 p = 4 u
9 p = 36

1 p = 36 ÷ 9 = 4

Number of pens in Box V in the end
= 10 p + 11 p
= 21 p
= 21 x 4
= 84

Answer(s): (a) 36; (b) 84