A total of 48 silver pencils and blue pencils are in a container. The ratio of silver pencils to blue pencils was 1 : 3. Some grey pencils and gold pencils were put into the container. For every 4 blue pencils that were already in the container, 12 gold ones were added. Then, the final number of silver pencils and grey pencils was ³₄ the final number of blue pencils and gold pencils. Find the total number of grey and gold pencils.

Grey pencils	Silver pencils	Blue pencils	Gold pencils
	1x4	3x4
		4x3	12x3
3x12		4x12
32 u	4 u	12 u	36 u

The number of blue pencils is repeated.  Make the number of blue pencils the same.  LCM of 3 and 4 is 12.

The total number of blue pencils and gold pencils is repeated.  Make the total number of blue and gold pencils the same.  LCM of 48 and 4 is 48.

Total number of silver pencils and blue pencils
= 4 u + 12 u
= 16 u

16 u = 48

1 u = 48 ÷ 16 = 3

Total number of grey and gold pencils
= 32 u + 36 u
= 68 u
= 68 x 3
= 204

Answer(s): 204