A total of 120 red punchers and purple punchers are in a container. The ratio of red punchers to purple punchers was 1 : 3. Some grey punchers and blue punchers were put into the container. For every 9 purple punchers that were already in the container, 6 blue ones were added. Then, the final number of red punchers and grey punchers was ²₃ the final number of purple punchers and blue punchers. Find the total number of grey and blue punchers.

Grey punchers	Red punchers	Purple punchers	Blue punchers
	1x3	3x3
		9x1	6x1
2x5		3x5
7 u	3 u	9 u	6 u

The number of purple punchers is repeated.  Make the number of purple punchers the same.  LCM of 3 and 9 is 9.

The total number of purple punchers and blue punchers is repeated.  Make the total number of purple and blue punchers the same.  LCM of 15 and 3 is 15.

Total number of red punchers and purple punchers
= 3 u + 9 u
= 12 u

12 u = 120

1 u = 120 ÷ 12 = 10

Total number of grey and blue punchers
= 7 u + 6 u
= 13 u
= 13 x 10
= 130

Answer(s): 130