A total of 143 gold pencils and purple pencils are in a container. The ratio of gold pencils to purple pencils was 4 : 9. Some green pencils and black pencils were put into the container. For every 3 purple pencils that were already in the container, 2 black ones were added. Then, the final number of gold pencils and green pencils was ⁴₅ the final number of purple pencils and black pencils. Find the total number of green and black pencils.

Green pencils	Gold pencils	Purple pencils	Black pencils
	4x1	9x1
		3x3	2x3
4x3		5x3
8 u	4 u	9 u	6 u

The number of purple pencils is repeated.  Make the number of purple pencils the same.  LCM of 9 and 3 is 9.

The total number of purple pencils and black pencils is repeated.  Make the total number of purple and black pencils the same.  LCM of 15 and 5 is 15.

Total number of gold pencils and purple pencils
= 4 u + 9 u
= 13 u

13 u = 143

1 u = 143 ÷ 13 = 11

Total number of green and black pencils
= 8 u + 6 u
= 14 u
= 14 x 11
= 154

Answer(s): 154