A total of 30 purple pens and brown pens are in a container. The ratio of purple pens to brown pens was 1 : 4. Some green pens and black pens were put into the container. For every 1 brown pens that were already in the container, 5 black ones were added. Then, the final number of purple pens and green pens was ³₈ the final number of brown pens and black pens. Find the total number of green and black pens.

Green pens	Purple pens	Brown pens	Black pens
	1x1	4x1
		1x4	5x4
3x3		8x3
8 u	1 u	4 u	20 u

The number of brown pens is repeated.  Make the number of brown pens the same.  LCM of 4 and 1 is 4.

The total number of brown pens and black pens is repeated.  Make the total number of brown and black pens the same.  LCM of 24 and 8 is 24.

Total number of purple pens and brown pens
= 1 u + 4 u
= 5 u

5 u = 30

1 u = 30 ÷ 5 = 6

Total number of green and black pens
= 8 u + 20 u
= 28 u
= 28 x 6
= 168

Answer(s): 168