A total of 20 blue rulers and silver rulers are in a container. The ratio of blue rulers to silver rulers was 1 : 4. Some gold rulers and yellow rulers were put into the container. For every 2 silver rulers that were already in the container, 16 yellow ones were added. Then, the final number of blue rulers and gold rulers was ¹₃ the final number of silver rulers and yellow rulers. Find the total number of gold and yellow rulers.

Gold rulers	Blue rulers	Silver rulers	Yellow rulers
	1x1	4x1
		2x2	16x2
1x12		3x12
11 u	1 u	4 u	32 u

The number of silver rulers is repeated.  Make the number of silver rulers the same.  LCM of 4 and 2 is 4.

The total number of silver rulers and yellow rulers is repeated.  Make the total number of silver and yellow rulers the same.  LCM of 36 and 3 is 36.

Total number of blue rulers and silver rulers
= 1 u + 4 u
= 5 u

5 u = 20

1 u = 20 ÷ 5 = 4

Total number of gold and yellow rulers
= 11 u + 32 u
= 43 u
= 43 x 4
= 172

Answer(s): 172