There were 113 green, silver and grey pens in a box. 17 grey pens were removed from the box and the ratio of the number of green pens to the number of silver pens to the number of grey pens became 2 : 3 : 7. Then some gold pens were added and the ratio of the number of grey pens to the number of gold pens was 7 : 2.

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

	Green	Silver	Grey	Gold	Total
Before	2 u	3 u	7 u + 17	0	113
Change 1	No change	No change	- 17		- 17
After 1	2 u	3 u	7 u		96
Change 2	No change	No change	No change	+ 2 u
After 2	2 u	3 u	7 u	2 u

(a)
Total number of pens at first
= 2 u + 3 u + 7 u + 17
= 12 u + 17

12 u + 17 = 113
12 u = 113 - 17
12 u = 96

1 u = 96 ÷ 12 = 8

Number of green pens at first
= 2 u
= 2 x 8
= 16

Number of silver pens at first
= 3 u
= 3 x 8
= 24

Number of grey pens at first
= 7 u + 17
= 7 x 8 + 17
= 73 

At first
Green pens : Silver pens : Grey pens
16 : 24 : 73

(b)
Total number of pens in the box in the end
= 2 u + 3 u + 7 u + 2 u
= 14 u
= 112

Answer(s): (a) 16 : 24 : 73; (b) 112