There were 196 gold, yellow and purple files in a box. 6 purple files were removed from the box and the ratio of the number of gold files to the number of yellow files to the number of purple files became 5 : 2 : 3. Then some silver files were added and the ratio of the number of purple files to the number of silver files was 3 : 7.

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

	Gold	Yellow	Purple	Silver	Total
Before	5 u	2 u	3 u + 6	0	196
Change 1	No change	No change	- 6		- 6
After 1	5 u	2 u	3 u		190
Change 2	No change	No change	No change	+ 7 u
After 2	5 u	2 u	3 u	7 u

(a)
Total number of files at first
= 5 u + 2 u + 3 u + 6
= 10 u + 6

10 u + 6 = 196
10 u = 196 - 6
10 u = 190

1 u = 190 ÷ 10 = 19

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

Number of yellow files at first
= 2 u
= 2 x 19
= 38

Number of purple files at first
= 3 u + 6
= 3 x 19 + 6
= 63 

At first
Gold files : Yellow files : Purple files
95 : 38 : 63

(b)
Total number of files in the box in the end
= 5 u + 2 u + 3 u + 7 u
= 17 u
= 323

Answer(s): (a) 95 : 38 : 63; (b) 323