There were 166 green, white and black notebooks in a box. 12 black notebooks were removed from the box and the ratio of the number of green notebooks to the number of white notebooks to the number of black notebooks became 3 : 2 : 9. Then some purple notebooks were added and the ratio of the number of black notebooks to the number of purple notebooks was 9 : 6.

1. What was the ratio of the number of green notebooks to the number of white notebooks to the number of black notebooks at first?
2. How many notebooks were in the box in the end?

	Green	White	Black	Purple	Total
Before	3 u	2 u	9 u + 12	0	166
Change 1	No change	No change	- 12		- 12
After 1	3 u	2 u	9 u		154
Change 2	No change	No change	No change	+ 6 u
After 2	3 u	2 u	9 u	6 u

(a)
Total number of notebooks at first
= 3 u + 2 u + 9 u + 12
= 14 u + 12

14 u + 12 = 166
14 u = 166 - 12
14 u = 154

1 u = 154 ÷ 14 = 11

Number of green notebooks at first
= 3 u
= 3 x 11
= 33

Number of white notebooks at first
= 2 u
= 2 x 11
= 22

Number of black notebooks at first
= 9 u + 12
= 9 x 11 + 12
= 111 

At first
Green notebooks : White notebooks : Black notebooks
33 : 22 : 111

(b)
Total number of notebooks in the box in the end
= 3 u + 2 u + 9 u + 6 u
= 20 u
= 220

Answer(s): (a) 33 : 22 : 111; (b) 220