A total of 56 red rulers and purple rulers are in a container. The ratio of red rulers to purple rulers was 1 : 6. Some silver rulers and yellow rulers were put into the container. For every 3 purple rulers that were already in the container, 13 yellow ones were added. Then, the final number of red rulers and silver rulers was ¹₈ the final number of purple rulers and yellow rulers. Find the total number of silver and yellow rulers.

Silver rulers	Red rulers	Purple rulers	Yellow rulers
	1x1	6x1
		3x2	13x2
1x4		8x4
3 u	1 u	6 u	26 u

The number of purple rulers is repeated.  Make the number of purple rulers the same.  LCM of 6 and 3 is 6.

The total number of purple rulers and yellow rulers is repeated.  Make the total number of purple and yellow rulers the same.  LCM of 32 and 8 is 32.

Total number of red rulers and purple rulers
= 1 u + 6 u
= 7 u

7 u = 56

1 u = 56 ÷ 7 = 8

Total number of silver and yellow rulers
= 3 u + 26 u
= 29 u
= 29 x 8
= 232

Answer(s): 232