A total of 105 red pens and black pens are in a container. The ratio of red pens to black pens was 1 : 4. Some green pens and yellow pens were put into the container. For every 7 black pens that were already in the container, 13 yellow ones were added. Then, the final number of red pens and green pens was ¹₈ the final number of black pens and yellow pens. Find the total number of green and yellow pens.

Green pens	Red pens	Black pens	Yellow pens
	1x7	4x7
		7x4	13x4
1x10		8x10
3 u	7 u	28 u	52 u

The number of black pens is repeated.  Make the number of black pens the same.  LCM of 4 and 7 is 28.

The total number of black pens and yellow pens is repeated.  Make the total number of black and yellow pens the same.  LCM of 80 and 8 is 80.

Total number of red pens and black pens
= 7 u + 28 u
= 35 u

35 u = 105

1 u = 105 ÷ 35 = 3

Total number of green and yellow pens
= 3 u + 52 u
= 55 u
= 55 x 3
= 165

Answer(s): 165