A total of 42 green pencils and pink pencils are in a container. The ratio of green pencils to pink pencils was 1 : 6. Some white pencils and purple pencils were put into the container. For every 1 pink pencils that were already in the container, 3 purple ones were added. Then, the final number of green pencils and white pencils was ¹₈ the final number of pink pencils and purple pencils. Find the total number of white and purple pencils.

White pencils	Green pencils	Pink pencils	Purple pencils
	1x1	6x1
		1x6	3x6
1x3		8x3
2 u	1 u	6 u	18 u

The number of pink pencils is repeated.  Make the number of pink pencils the same.  LCM of 6 and 1 is 6.

The total number of pink pencils and purple pencils is repeated.  Make the total number of pink and purple pencils the same.  LCM of 24 and 8 is 24.

Total number of green pencils and pink pencils
= 1 u + 6 u
= 7 u

7 u = 42

1 u = 42 ÷ 7 = 6

Total number of white and purple pencils
= 2 u + 18 u
= 20 u
= 20 x 6
= 120

Answer(s): 120