There were 223 blue, red and pink files in a box. 7 pink files were removed from the box and the ratio of the number of blue files to the number of red files to the number of pink files became 3 : 4 : 5. Then some white files were added and the ratio of the number of pink files to the number of white files was 5 : 4.

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

	Blue	Red	Pink	White	Total
Before	3 u	4 u	5 u + 7	0	223
Change 1	No change	No change	- 7		- 7
After 1	3 u	4 u	5 u		216
Change 2	No change	No change	No change	+ 4 u
After 2	3 u	4 u	5 u	4 u

(a)
Total number of files at first
= 3 u + 4 u + 5 u + 7
= 12 u + 7

12 u + 7 = 223
12 u = 223 - 7
12 u = 216

1 u = 216 ÷ 12 = 18

Number of blue files at first
= 3 u
= 3 x 18
= 54

Number of red files at first
= 4 u
= 4 x 18
= 72

Number of pink files at first
= 5 u + 7
= 5 x 18 + 7
= 97 

At first
Blue files : Red files : Pink files
54 : 72 : 97

(b)
Total number of files in the box in the end
= 3 u + 4 u + 5 u + 4 u
= 16 u
= 288

Answer(s): (a) 54 : 72 : 97; (b) 288