A convenience store sold salmon, bacon and tuna sandwiches. The ratio of the number of salmon sandwiches made to the total number of sandwiches made was 4 : 9. The ratio of the number of bacon sandwiches made to the total number of sandwiches made was 1 : 5. After the store sold some salmon sandwiches and made another 9 bacon sandwiches, there was an equal number of salmon, bacon and tuna sandwiches left. Find the number of salmon sandwiches sold.

	Salmon	Bacon	Tuna	Total
Comparing salmon to total	4x5			9x5
Comparing  bacon to total		1x9		5x9
	20 u	9 u	16 u	45 u

	Salmon	Bacon	Tuna	Total
Before	20 u	9 u	16 u	45 u
Change	- 4 u	+ 9	No change
After	1x16 = 16 u	1x16 = 16 u	1x16 = 16 u

The total number of sandwiches is the same at first. Make the total number of sandwiches the same.  LCM of 5 and 9 is 45.

Number of tuna sandwiches remains the same at first and in the end. Make the number of tuna sandwiches the  same. LCM of 1 and 16 is 16.

Number of tuna sandwiches 
= 45 u - 20 u - 9 u
= 16 u

Number of salmon, bacon and tuna sandwiches is the same in the end. 

Number of bacon sandwiches = 9 u + 9

9 u + 9 = 16 u
16 u - 9 u = 9
7 u = 9

1 u = 9 ÷ 7 = 8

Number of salmon sandwiches sold
= 20 u - 16 u
= 4 u
= 4 x 8
= 32

Answer(s): 32