There were 83 brown, white and grey pens in a box. 2 grey pens were removed from the box and the ratio of the number of brown pens to the number of white pens to the number of grey pens became 4 : 2 : 3. Then some silver pens were added and the ratio of the number of grey pens to the number of silver pens was 3 : 7.

1. What was the ratio of the number of brown pens to the number of white pens to the number of grey pens at first?
2. How many pens were in the box in the end?

	Brown	White	Grey	Silver	Total
Before	4 u	2 u	3 u + 2	0	83
Change 1	No change	No change	- 2		- 2
After 1	4 u	2 u	3 u		81
Change 2	No change	No change	No change	+ 7 u
After 2	4 u	2 u	3 u	7 u

(a)
Total number of pens at first
= 4 u + 2 u + 3 u + 2
= 9 u + 2

9 u + 2 = 83
9 u = 83 - 2
9 u = 81

1 u = 81 ÷ 9 = 9

Number of brown pens at first
= 4 u
= 4 x 9
= 36

Number of white pens at first
= 2 u
= 2 x 9
= 18

Number of grey pens at first
= 3 u + 2
= 3 x 9 + 2
= 29 

At first
Brown pens : White pens : Grey pens
36 : 18 : 29

(b)
Total number of pens in the box in the end
= 4 u + 2 u + 3 u + 7 u
= 16 u
= 144

Answer(s): (a) 36 : 18 : 29; (b) 144