A total of 21 black folders and red folders are in a container. The ratio of black folders to red folders was 1 : 6. Some white folders and grey folders were put into the container. For every 3 red folders that were already in the container, 9 grey ones were added. Then, the final number of black folders and white folders was ¹₄ the final number of red folders and grey folders. Find the total number of white and grey folders.

White folders	Black folders	Red folders	Grey folders
	1x1	6x1
		3x2	9x2
1x6		4x6
5 u	1 u	6 u	18 u

The number of red folders is repeated.  Make the number of red folders the same.  LCM of 6 and 3 is 6.

The total number of red folders and grey folders is repeated.  Make the total number of red and grey folders the same.  LCM of 24 and 4 is 24.

Total number of black folders and red folders
= 1 u + 6 u
= 7 u

7 u = 21

1 u = 21 ÷ 7 = 3

Total number of white and grey folders
= 5 u + 18 u
= 23 u
= 23 x 3
= 69

Answer(s): 69