A total of 22 yellow pens and gold pens are in a container. The ratio of yellow pens to gold pens was 3 : 8. Some white pens and red pens were put into the container. For every 4 gold pens that were already in the container, 7 red ones were added. Then, the final number of yellow pens and white pens was ¹₂ the final number of gold pens and red pens. Find the total number of white and red pens.

White pens	Yellow pens	Gold pens	Red pens
	3x1	8x1
		4x2	7x2
1x11		2x11
8 u	3 u	8 u	14 u

The number of gold pens is repeated.  Make the number of gold pens the same.  LCM of 8 and 4 is 8.

The total number of gold pens and red pens is repeated.  Make the total number of gold and red pens the same.  LCM of 22 and 2 is 22.

Total number of yellow pens and gold pens
= 3 u + 8 u
= 11 u

11 u = 22

1 u = 22 ÷ 11 = 2

Total number of white and red pens
= 8 u + 14 u
= 22 u
= 22 x 2
= 44

Answer(s): 44