There were 102 white, brown and grey files in a box. 22 grey files were removed from the box and the ratio of the number of white files to the number of brown files to the number of grey files became 4 : 5 : 7. Then some red files were added and the ratio of the number of grey files to the number of red files was 7 : 3.

1. What was the ratio of the number of white 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?

	White	Brown	Grey	Red	Total
Before	4 u	5 u	7 u + 22	0	102
Change 1	No change	No change	- 22		- 22
After 1	4 u	5 u	7 u		80
Change 2	No change	No change	No change	+ 3 u
After 2	4 u	5 u	7 u	3 u

(a)
Total number of files at first
= 4 u + 5 u + 7 u + 22
= 16 u + 22

16 u + 22 = 102
16 u = 102 - 22
16 u = 80

1 u = 80 ÷ 16 = 5

Number of white files at first
= 4 u
= 4 x 5
= 20

Number of brown files at first
= 5 u
= 5 x 5
= 25

Number of grey files at first
= 7 u + 22
= 7 x 5 + 22
= 57 

At first
White files : Brown files : Grey files
20 : 25 : 57

(b)
Total number of files in the box in the end
= 4 u + 5 u + 7 u + 3 u
= 19 u
= 95

Answer(s): (a) 20 : 25 : 57; (b) 95