There were 103 grey, white and red notebooks in a box. 19 red 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 red notebooks became 5 : 4 : 3. Then some purple notebooks were added and the ratio of the number of red notebooks to the number of purple notebooks was 3 : 2.

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

	Grey	White	Red	Purple	Total
Before	5 u	4 u	3 u + 19	0	103
Change 1	No change	No change	- 19		- 19
After 1	5 u	4 u	3 u		84
Change 2	No change	No change	No change	+ 2 u
After 2	5 u	4 u	3 u	2 u

(a)
Total number of notebooks at first
= 5 u + 4 u + 3 u + 19
= 12 u + 19

12 u + 19 = 103
12 u = 103 - 19
12 u = 84

1 u = 84 ÷ 12 = 7

Number of grey notebooks at first
= 5 u
= 5 x 7
= 35

Number of white notebooks at first
= 4 u
= 4 x 7
= 28

Number of red notebooks at first
= 3 u + 19
= 3 x 7 + 19
= 40 

At first
Grey notebooks : White notebooks : Red notebooks
35 : 28 : 40

(b)
Total number of notebooks in the box in the end
= 5 u + 4 u + 3 u + 2 u
= 14 u
= 98

Answer(s): (a) 35 : 28 : 40; (b) 98