There were 336 silver, brown and grey files in a box. 13 grey files were removed from the box and the ratio of the number of silver files to the number of brown files to the number of grey files became 3 : 5 : 9. Then some green files were added and the ratio of the number of grey files to the number of green files was 9 : 5.

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

	Silver	Brown	Grey	Green	Total
Before	3 u	5 u	9 u + 13	0	336
Change 1	No change	No change	- 13		- 13
After 1	3 u	5 u	9 u		323
Change 2	No change	No change	No change	+ 5 u
After 2	3 u	5 u	9 u	5 u

(a)
Total number of files at first
= 3 u + 5 u + 9 u + 13
= 17 u + 13

17 u + 13 = 336
17 u = 336 - 13
17 u = 323

1 u = 323 ÷ 17 = 19

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

Number of brown files at first
= 5 u
= 5 x 19
= 95

Number of grey files at first
= 9 u + 13
= 9 x 19 + 13
= 184 

At first
Silver files : Brown files : Grey files
57 : 95 : 184

(b)
Total number of files in the box in the end
= 3 u + 5 u + 9 u + 5 u
= 22 u
= 418

Answer(s): (a) 57 : 95 : 184; (b) 418