A total of 105 purple rulers and brown rulers are in a container. The ratio of purple rulers to brown rulers was 1 : 4. Some black rulers and blue rulers were put into the container. For every 7 brown rulers that were already in the container, 3 blue ones were added. Then, the final number of purple rulers and black rulers was ³₈ the final number of brown rulers and blue rulers. Find the total number of black and blue rulers.

Black rulers	Purple rulers	Brown rulers	Blue rulers
	1x7	4x7
		7x4	3x4
3x5		8x5
8 u	7 u	28 u	12 u

The number of brown rulers is repeated.  Make the number of brown rulers the same.  LCM of 4 and 7 is 28.

The total number of brown rulers and blue rulers is repeated.  Make the total number of brown and blue rulers the same.  LCM of 40 and 8 is 40.

Total number of purple rulers and brown rulers
= 7 u + 28 u
= 35 u

35 u = 105

1 u = 105 ÷ 35 = 3

Total number of black and blue rulers
= 8 u + 12 u
= 20 u
= 20 x 3
= 60

Answer(s): 60