There were 179 white, silver and black files in a box. 10 black files were removed from the box and the ratio of the number of white files to the number of silver files to the number of black files became 2 : 4 : 7. Then some pink files were added and the ratio of the number of black files to the number of pink files was 7 : 3.

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

	White	Silver	Black	Pink	Total
Before	2 u	4 u	7 u + 10	0	179
Change 1	No change	No change	- 10		- 10
After 1	2 u	4 u	7 u		169
Change 2	No change	No change	No change	+ 3 u
After 2	2 u	4 u	7 u	3 u

(a)
Total number of files at first
= 2 u + 4 u + 7 u + 10
= 13 u + 10

13 u + 10 = 179
13 u = 179 - 10
13 u = 169

1 u = 169 ÷ 13 = 13

Number of white files at first
= 2 u
= 2 x 13
= 26

Number of silver files at first
= 4 u
= 4 x 13
= 52

Number of black files at first
= 7 u + 10
= 7 x 13 + 10
= 101 

At first
White files : Silver files : Black files
26 : 52 : 101

(b)
Total number of files in the box in the end
= 2 u + 4 u + 7 u + 3 u
= 16 u
= 208

Answer(s): (a) 26 : 52 : 101; (b) 208