There were 250 red, gold and pink files in a box. 22 pink files were removed from the box and the ratio of the number of red files to the number of gold files to the number of pink files became 4 : 5 : 3. Then some black files were added and the ratio of the number of pink files to the number of black files was 3 : 7.

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

	Red	Gold	Pink	Black	Total
Before	4 u	5 u	3 u + 22	0	250
Change 1	No change	No change	- 22		- 22
After 1	4 u	5 u	3 u		228
Change 2	No change	No change	No change	+ 7 u
After 2	4 u	5 u	3 u	7 u

(a)
Total number of files at first
= 4 u + 5 u + 3 u + 22
= 12 u + 22

12 u + 22 = 250
12 u = 250 - 22
12 u = 228

1 u = 228 ÷ 12 = 19

Number of red files at first
= 4 u
= 4 x 19
= 76

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

Number of pink files at first
= 3 u + 22
= 3 x 19 + 22
= 79 

At first
Red files : Gold files : Pink files
76 : 95 : 79

(b)
Total number of files in the box in the end
= 4 u + 5 u + 3 u + 7 u
= 19 u
= 361

Answer(s): (a) 76 : 95 : 79; (b) 361