A convenience store sold tuna, ham and salmon 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 ham sandwiches made to the total number of sandwiches made was 1 : 8. After the store sold some tuna sandwiches and made another 13 ham sandwiches, there was an equal number of tuna, ham and salmon sandwiches left. Find the number of tuna sandwiches sold.

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

	Tuna	Ham	Salmon	Total
Before	16 u	3 u	5 u	24 u
Change	- 11 u	+ 13	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 salmon sandwiches remains the same at first and in the end. Make the number of salmon sandwiches the  same. LCM of 1 and 5 is 5.

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

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

Number of ham sandwiches = 3 u + 13

3 u + 13 = 5 u
5 u - 3 u = 13
2 u = 13

1 u = 13 ÷ 2 = 2

Number of tuna sandwiches sold
= 16 u - 5 u
= 11 u
= 11 x 2
= 22

Answer(s): 22