A total of 64 green notebooks and black notebooks are in a container. The ratio of green notebooks to black notebooks was 1 : 3. Some gold notebooks and purple notebooks were put into the container. For every 8 black notebooks that were already in the container, 6 purple ones were added. Then, the final number of green notebooks and gold notebooks was ⁵₇ the final number of black notebooks and purple notebooks. Find the total number of gold and purple notebooks.

Gold notebooks	Green notebooks	Black notebooks	Purple notebooks
	1x8	3x8
		8x3	6x3
5x6		7x6
22 u	8 u	24 u	18 u

The number of black notebooks is repeated.  Make the number of black notebooks the same.  LCM of 3 and 8 is 24.

The total number of black notebooks and purple notebooks is repeated.  Make the total number of black and purple notebooks the same.  LCM of 42 and 7 is 42.

Total number of green notebooks and black notebooks
= 8 u + 24 u
= 32 u

32 u = 64

1 u = 64 ÷ 32 = 2

Total number of gold and purple notebooks
= 22 u + 18 u
= 40 u
= 40 x 2
= 80

Answer(s): 80