There were 107 black, silver and green notebooks in a box. 23 green notebooks were removed from the box and the ratio of the number of black notebooks to the number of silver notebooks to the number of green notebooks became 3 : 4 : 7. Then some white notebooks were added and the ratio of the number of green notebooks to the number of white notebooks was 7 : 2.

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

	Black	Silver	Green	White	Total
Before	3 u	4 u	7 u + 23	0	107
Change 1	No change	No change	- 23		- 23
After 1	3 u	4 u	7 u		84
Change 2	No change	No change	No change	+ 2 u
After 2	3 u	4 u	7 u	2 u

(a)
Total number of notebooks at first
= 3 u + 4 u + 7 u + 23
= 14 u + 23

14 u + 23 = 107
14 u = 107 - 23
14 u = 84

1 u = 84 ÷ 14 = 6

Number of black notebooks at first
= 3 u
= 3 x 6
= 18

Number of silver notebooks at first
= 4 u
= 4 x 6
= 24

Number of green notebooks at first
= 7 u + 23
= 7 x 6 + 23
= 65 

At first
Black notebooks : Silver notebooks : Green notebooks
18 : 24 : 65

(b)
Total number of notebooks in the box in the end
= 3 u + 4 u + 7 u + 2 u
= 16 u
= 96

Answer(s): (a) 18 : 24 : 65; (b) 96