A total of 70 brown pencils and silver pencils are in a container. The ratio of brown pencils to silver pencils was 1 : 4. Some gold pencils and purple pencils were put into the container. For every 7 silver pencils that were already in the container, 11 purple ones were added. Then, the final number of brown pencils and gold pencils was ³₈ the final number of silver pencils and purple pencils. Find the total number of gold and purple pencils.

Gold pencils	Brown pencils	Silver pencils	Purple pencils
	1x7	4x7
		7x4	11x4
3x9		8x9
20 u	7 u	28 u	44 u

The number of silver pencils is repeated.  Make the number of silver pencils the same.  LCM of 4 and 7 is 28.

The total number of silver pencils and purple pencils is repeated.  Make the total number of silver and purple pencils the same.  LCM of 72 and 8 is 72.

Total number of brown pencils and silver pencils
= 7 u + 28 u
= 35 u

35 u = 70

1 u = 70 ÷ 35 = 2

Total number of gold and purple pencils
= 20 u + 44 u
= 64 u
= 64 x 2
= 128

Answer(s): 128