There were 305 blue, black and green files in a box. 17 green files were removed from the box and the ratio of the number of blue files to the number of black files to the number of green files became 5 : 4 : 7. Then some purple files were added and the ratio of the number of green files to the number of purple files was 7 : 7.

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

	Blue	Black	Green	Purple	Total
Before	5 u	4 u	7 u + 17	0	305
Change 1	No change	No change	- 17		- 17
After 1	5 u	4 u	7 u		288
Change 2	No change	No change	No change	+ 7 u
After 2	5 u	4 u	7 u	7 u

(a)
Total number of files at first
= 5 u + 4 u + 7 u + 17
= 16 u + 17

16 u + 17 = 305
16 u = 305 - 17
16 u = 288

1 u = 288 ÷ 16 = 18

Number of blue files at first
= 5 u
= 5 x 18
= 90

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

Number of green files at first
= 7 u + 17
= 7 x 18 + 17
= 143 

At first
Blue files : Black files : Green files
90 : 72 : 143

(b)
Total number of files in the box in the end
= 5 u + 4 u + 7 u + 7 u
= 23 u
= 414

Answer(s): (a) 90 : 72 : 143; (b) 414