A total of 45 red staplers and black staplers are in a container. The ratio of red staplers to black staplers was 1 : 2. Some purple staplers and gold staplers were put into the container. For every 6 black staplers that were already in the container, 6 gold ones were added. Then, the final number of red staplers and purple staplers was ²₃ the final number of black staplers and gold staplers. Find the total number of purple and gold staplers.

Purple staplers	Red staplers	Black staplers	Gold staplers
	1x3	2x3
		6x1	6x1
2x4		3x4
5 u	3 u	6 u	6 u

The number of black staplers is repeated.  Make the number of black staplers the same.  LCM of 2 and 6 is 6.

The total number of black staplers and gold staplers is repeated.  Make the total number of black and gold staplers the same.  LCM of 12 and 3 is 12.

Total number of red staplers and black staplers
= 3 u + 6 u
= 9 u

9 u = 45

1 u = 45 ÷ 9 = 5

Total number of purple and gold staplers
= 5 u + 6 u
= 11 u
= 11 x 5
= 55

Answer(s): 55