A convenience store sold tuna, salmon and chicken sandwiches. The ratio of the number of tuna sandwiches made to the total number of sandwiches made was 2 : 3. The ratio of the number of salmon sandwiches made to the total number of sandwiches made was 1 : 8. After the store sold some tuna sandwiches and made another 19 salmon sandwiches, there was an equal number of tuna, salmon and chicken sandwiches left. Find the number of tuna sandwiches sold.

	Tuna	Salmon	Chicken	Total
Comparing tuna to total	2x8			3x8
Comparing  salmon to total		1x3		8x3
	16 u	3 u	5 u	24 u

	Tuna	Salmon	Chicken	Total
Before	16 u	3 u	5 u	24 u
Change	- 11 u	+ 19	No change
After	1x5 = 5 u	1x5 = 5 u	1x5 = 5 u

The total number of sandwiches is the same at first. Make the total number of sandwiches the same.  LCM of 8 and 3 is 24.

Number of chicken sandwiches remains the same at first and in the end. Make the number of chicken sandwiches the  same. LCM of 1 and 5 is 5.

Number of chicken sandwiches 
= 24 u - 16 u - 3 u
= 5 u

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

Number of salmon sandwiches = 3 u + 19

3 u + 19 = 5 u
5 u - 3 u = 19
2 u = 19

1 u = 19 ÷ 2 = 4

Number of tuna sandwiches sold
= 16 u - 5 u
= 11 u
= 11 x 4
= 44

Answer(s): 44