There were 149 grey, black and blue files in a box. 5 blue files were removed from the box and the ratio of the number of grey files to the number of black files to the number of blue files became 3 : 2 : 7. Then some silver files were added and the ratio of the number of blue files to the number of silver files was 7 : 8.

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

	Grey	Black	Blue	Silver	Total
Before	3 u	2 u	7 u + 5	0	149
Change 1	No change	No change	- 5		- 5
After 1	3 u	2 u	7 u		144
Change 2	No change	No change	No change	+ 8 u
After 2	3 u	2 u	7 u	8 u

(a)
Total number of files at first
= 3 u + 2 u + 7 u + 5
= 12 u + 5

12 u + 5 = 149
12 u = 149 - 5
12 u = 144

1 u = 144 ÷ 12 = 12

Number of grey files at first
= 3 u
= 3 x 12
= 36

Number of black files at first
= 2 u
= 2 x 12
= 24

Number of blue files at first
= 7 u + 5
= 7 x 12 + 5
= 89 

At first
Grey files : Black files : Blue files
36 : 24 : 89

(b)
Total number of files in the box in the end
= 3 u + 2 u + 7 u + 8 u
= 20 u
= 240

Answer(s): (a) 36 : 24 : 89; (b) 240