A convenience store sold club, salmon and tuna sandwiches. The ratio of the number of club 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 club sandwiches and made another 23 salmon sandwiches, there was an equal number of club, salmon and tuna sandwiches left. Find the number of club sandwiches sold.

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

	Club	Salmon	Tuna	Total
Before	16 u	3 u	5 u	24 u
Change	- 11 u	+ 23	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 tuna sandwiches remains the same at first and in the end. Make the number of tuna sandwiches the  same. LCM of 1 and 5 is 5.

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

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

Number of salmon sandwiches = 3 u + 23

3 u + 23 = 5 u
5 u - 3 u = 23
2 u = 23

1 u = 23 ÷ 2 = 2

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

Answer(s): 22