A total of 63 pink pens and green pens are in a container. The ratio of pink pens to green pens was 1 : 6. Some purple pens and red pens were put into the container. For every 9 green pens that were already in the container, 12 red ones were added. Then, the final number of pink pens and purple pens was ⁵₇ the final number of green pens and red pens. Find the total number of purple and red pens.

Purple pens	Pink pens	Green pens	Red pens
	1x3	6x3
		9x2	12x2
5x6		7x6
27 u	3 u	18 u	24 u

The number of green pens is repeated.  Make the number of green pens the same.  LCM of 6 and 9 is 18.

The total number of green pens and red pens is repeated.  Make the total number of green and red pens the same.  LCM of 42 and 7 is 42.

Total number of pink pens and green pens
= 3 u + 18 u
= 21 u

21 u = 63

1 u = 63 ÷ 21 = 3

Total number of purple and red pens
= 27 u + 24 u
= 51 u
= 51 x 3
= 153

Answer(s): 153