A total of 54 red files and purple files are in a container. The ratio of red files to purple files was 1 : 2. Some silver files and white files were put into the container. For every 9 purple files that were already in the container, 11 white ones were added. Then, the final number of red files and silver files was ²₅ the final number of purple files and white files. Find the total number of silver and white files.

Silver files	Red files	Purple files	White files
	1x9	2x9
		9x2	11x2
2x8		5x8
7 u	9 u	18 u	22 u

The number of purple files is repeated.  Make the number of purple files the same.  LCM of 2 and 9 is 18.

The total number of purple files and white files is repeated.  Make the total number of purple and white files the same.  LCM of 40 and 5 is 40.

Total number of red files and purple files
= 9 u + 18 u
= 27 u

27 u = 54

1 u = 54 ÷ 27 = 2

Total number of silver and white files
= 7 u + 22 u
= 29 u
= 29 x 2
= 58

Answer(s): 58