There were 131 pink, black and gold files in a box. 14 gold files were removed from the box and the ratio of the number of pink files to the number of black files to the number of gold files became 4 : 2 : 3. Then some blue files were added and the ratio of the number of gold files to the number of blue files was 3 : 5.

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

	Pink	Black	Gold	Blue	Total
Before	4 u	2 u	3 u + 14	0	131
Change 1	No change	No change	- 14		- 14
After 1	4 u	2 u	3 u		117
Change 2	No change	No change	No change	+ 5 u
After 2	4 u	2 u	3 u	5 u

(a)
Total number of files at first
= 4 u + 2 u + 3 u + 14
= 9 u + 14

9 u + 14 = 131
9 u = 131 - 14
9 u = 117

1 u = 117 ÷ 9 = 13

Number of pink files at first
= 4 u
= 4 x 13
= 52

Number of black files at first
= 2 u
= 2 x 13
= 26

Number of gold files at first
= 3 u + 14
= 3 x 13 + 14
= 53 

At first
Pink files : Black files : Gold files
52 : 26 : 53

(b)
Total number of files in the box in the end
= 4 u + 2 u + 3 u + 5 u
= 14 u
= 182

Answer(s): (a) 52 : 26 : 53; (b) 182