There were 209 red, green and grey files in a box. 9 grey files were removed from the box and the ratio of the number of red files to the number of green files to the number of grey files became 3 : 2 : 5. Then some gold files were added and the ratio of the number of grey files to the number of gold files was 5 : 4.

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

	Red	Green	Grey	Gold	Total
Before	3 u	2 u	5 u + 9	0	209
Change 1	No change	No change	- 9		- 9
After 1	3 u	2 u	5 u		200
Change 2	No change	No change	No change	+ 4 u
After 2	3 u	2 u	5 u	4 u

(a)
Total number of files at first
= 3 u + 2 u + 5 u + 9
= 10 u + 9

10 u + 9 = 209
10 u = 209 - 9
10 u = 200

1 u = 200 ÷ 10 = 20

Number of red files at first
= 3 u
= 3 x 20
= 60

Number of green files at first
= 2 u
= 2 x 20
= 40

Number of grey files at first
= 5 u + 9
= 5 x 20 + 9
= 109 

At first
Red files : Green files : Grey files
60 : 40 : 109

(b)
Total number of files in the box in the end
= 3 u + 2 u + 5 u + 4 u
= 14 u
= 280

Answer(s): (a) 60 : 40 : 109; (b) 280