There were 274 silver, purple and white notebooks in a box. 8 white notebooks were removed from the box and the ratio of the number of silver notebooks to the number of purple notebooks to the number of white notebooks became 3 : 4 : 7. Then some grey notebooks were added and the ratio of the number of white notebooks to the number of grey notebooks was 7 : 8.

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

	Silver	Purple	White	Grey	Total
Before	3 u	4 u	7 u + 8	0	274
Change 1	No change	No change	- 8		- 8
After 1	3 u	4 u	7 u		266
Change 2	No change	No change	No change	+ 8 u
After 2	3 u	4 u	7 u	8 u

(a)
Total number of notebooks at first
= 3 u + 4 u + 7 u + 8
= 14 u + 8

14 u + 8 = 274
14 u = 274 - 8
14 u = 266

1 u = 266 ÷ 14 = 19

Number of silver notebooks at first
= 3 u
= 3 x 19
= 57

Number of purple notebooks at first
= 4 u
= 4 x 19
= 76

Number of white notebooks at first
= 7 u + 8
= 7 x 19 + 8
= 141 

At first
Silver notebooks : Purple notebooks : White notebooks
57 : 76 : 141

(b)
Total number of notebooks in the box in the end
= 3 u + 4 u + 7 u + 8 u
= 22 u
= 418

Answer(s): (a) 57 : 76 : 141; (b) 418