There were 57 grey, white and blue notebooks in a box. 12 blue notebooks were removed from the box and the ratio of the number of grey notebooks to the number of white notebooks to the number of blue notebooks became 4 : 2 : 3. Then some pink notebooks were added and the ratio of the number of blue notebooks to the number of pink notebooks was 3 : 7.

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

	Grey	White	Blue	Pink	Total
Before	4 u	2 u	3 u + 12	0	57
Change 1	No change	No change	- 12		- 12
After 1	4 u	2 u	3 u		45
Change 2	No change	No change	No change	+ 7 u
After 2	4 u	2 u	3 u	7 u

(a)
Total number of notebooks at first
= 4 u + 2 u + 3 u + 12
= 9 u + 12

9 u + 12 = 57
9 u = 57 - 12
9 u = 45

1 u = 45 ÷ 9 = 5

Number of grey notebooks at first
= 4 u
= 4 x 5
= 20

Number of white notebooks at first
= 2 u
= 2 x 5
= 10

Number of blue notebooks at first
= 3 u + 12
= 3 x 5 + 12
= 27 

At first
Grey notebooks : White notebooks : Blue notebooks
20 : 10 : 27

(b)
Total number of notebooks in the box in the end
= 4 u + 2 u + 3 u + 7 u
= 16 u
= 80

Answer(s): (a) 20 : 10 : 27; (b) 80