A total of 30 yellow folders and purple folders are in a container. The ratio of yellow folders to purple folders was 1 : 9. Some red folders and brown folders were put into the container. For every 1 purple folders that were already in the container, 6 brown ones were added. Then, the final number of yellow folders and red folders was ³₇ the final number of purple folders and brown folders. Find the total number of red and brown folders.

Red folders	Yellow folders	Purple folders	Brown folders
	1x1	9x1
		1x9	6x9
3x9		7x9
26 u	1 u	9 u	54 u

The number of purple folders is repeated.  Make the number of purple folders the same.  LCM of 9 and 1 is 9.

The total number of purple folders and brown folders is repeated.  Make the total number of purple and brown folders the same.  LCM of 63 and 7 is 63.

Total number of yellow folders and purple folders
= 1 u + 9 u
= 10 u

10 u = 30

1 u = 30 ÷ 10 = 3

Total number of red and brown folders
= 26 u + 54 u
= 80 u
= 80 x 3
= 240

Answer(s): 240