A total of 44 blue rulers and black rulers are in a container. The ratio of blue rulers to black rulers was 2 : 9. Some pink rulers and silver rulers were put into the container. For every 3 black rulers that were already in the container, 13 silver ones were added. Then, the final number of blue rulers and pink rulers was ¹₈ the final number of black rulers and silver rulers. Find the total number of pink and silver rulers.

Pink rulers	Blue rulers	Black rulers	Silver rulers
	2x1	9x1
		3x3	13x3
1x6		8x6
4 u	2 u	9 u	39 u

The number of black rulers is repeated.  Make the number of black rulers the same.  LCM of 9 and 3 is 9.

The total number of black rulers and silver rulers is repeated.  Make the total number of black and silver rulers the same.  LCM of 48 and 8 is 48.

Total number of blue rulers and black rulers
= 2 u + 9 u
= 11 u

11 u = 44

1 u = 44 ÷ 11 = 4

Total number of pink and silver rulers
= 4 u + 39 u
= 43 u
= 43 x 4
= 172

Answer(s): 172