A total of 40 grey staplers and purple staplers are in a container. The ratio of grey staplers to purple staplers was 1 : 9. Some red staplers and black staplers were put into the container. For every 6 purple staplers that were already in the container, 8 black ones were added. Then, the final number of grey staplers and red staplers was ²₇ the final number of purple staplers and black staplers. Find the total number of red and black staplers.

Red staplers	Grey staplers	Purple staplers	Black staplers
	1x2	9x2
		6x3	8x3
2x6		7x6
10 u	2 u	18 u	24 u

The number of purple staplers is repeated.  Make the number of purple staplers the same.  LCM of 9 and 6 is 18.

The total number of purple staplers and black staplers is repeated.  Make the total number of purple and black staplers the same.  LCM of 42 and 7 is 42.

Total number of grey staplers and purple staplers
= 2 u + 18 u
= 20 u

20 u = 40

1 u = 40 ÷ 20 = 2

Total number of red and black staplers
= 10 u + 24 u
= 34 u
= 34 x 2
= 68

Answer(s): 68