A convenience store sold salmon, club and tuna sandwiches. The ratio of the number of salmon sandwiches made to the total number of sandwiches made was 1 : 2. The ratio of the number of club sandwiches made to the total number of sandwiches made was 1 : 7. After the store sold some salmon sandwiches and made another 9 club sandwiches, there was an equal number of salmon, club and tuna sandwiches left. Find the number of salmon sandwiches sold.

	Salmon	Club	Tuna	Total
Comparing salmon to total	1x7			2x7
Comparing  club to total		1x2		7x2
	7 u	2 u	5 u	14 u

	Salmon	Club	Tuna	Total
Before	7 u	2 u	5 u	14 u
Change	- 2 u	+ 9	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 7 and 2 is 14.

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 
= 14 u - 7 u - 2 u
= 5 u

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

Number of club sandwiches = 2 u + 9

2 u + 9 = 5 u
5 u - 2 u = 9
3 u = 9

1 u = 9 ÷ 3 = 7

Number of salmon sandwiches sold
= 7 u - 5 u
= 2 u
= 2 x 7
= 14

Answer(s): 14