A total of 48 purple files and yellow files are in a container. The ratio of purple files to yellow files was 1 : 2. Some blue files and pink files were put into the container. For every 8 yellow files that were already in the container, 6 pink ones were added. Then, the final number of purple files and blue files was ³₇ the final number of yellow files and pink files. Find the total number of blue and pink files.

Blue files	Purple files	Yellow files	Pink files
	1x4	2x4
		8x1	6x1
3x2		7x2
2 u	4 u	8 u	6 u

The number of yellow files is repeated.  Make the number of yellow files the same.  LCM of 2 and 8 is 8.

The total number of yellow files and pink files is repeated.  Make the total number of yellow and pink files the same.  LCM of 14 and 7 is 14.

Total number of purple files and yellow files
= 4 u + 8 u
= 12 u

12 u = 48

1 u = 48 ÷ 12 = 4

Total number of blue and pink files
= 2 u + 6 u
= 8 u
= 8 x 4
= 32

Answer(s): 32