A total of 15 black punchers and purple punchers are in a container. The ratio of black punchers to purple punchers was 1 : 4. Some silver punchers and gold punchers were put into the container. For every 2 purple punchers that were already in the container, 12 gold ones were added. Then, the final number of black punchers and silver punchers was ⁶₇ the final number of purple punchers and gold punchers. Find the total number of silver and gold punchers.

Silver punchers	Black punchers	Purple punchers	Gold punchers
	1x1	4x1
		2x2	12x2
6x4		7x4
23 u	1 u	4 u	24 u

The number of purple punchers is repeated.  Make the number of purple punchers the same.  LCM of 4 and 2 is 4.

The total number of purple punchers and gold punchers is repeated.  Make the total number of purple and gold punchers the same.  LCM of 28 and 7 is 28.

Total number of black punchers and purple punchers
= 1 u + 4 u
= 5 u

5 u = 15

1 u = 15 ÷ 5 = 3

Total number of silver and gold punchers
= 23 u + 24 u
= 47 u
= 47 x 3
= 141

Answer(s): 141