A convenience store sold salmon, club and egg mayo sandwiches. The ratio of the number of salmon sandwiches made to the total number of sandwiches made was 4 : 7. The ratio of the number of club sandwiches made to the total number of sandwiches made was 1 : 6. After the store sold some salmon sandwiches and made another 12 club sandwiches, there was an equal number of salmon, club and egg mayo sandwiches left. Find the number of salmon sandwiches sold.

	Salmon	Club	Egg Mayo	Total
Comparing salmon to total	4x6			7x6
Comparing  club to total		1x7		6x7
	24 u	7 u	11 u	42 u

	Salmon	Club	Egg Mayo	Total
Before	24 u	7 u	11 u	42 u
Change	- 13 u	+ 12	No change
After	1x11 = 11 u	1x11 = 11 u	1x11 = 11 u

The total number of sandwiches is the same at first. Make the total number of sandwiches the same.  LCM of 6 and 7 is 42.

Number of egg mayo sandwiches remains the same at first and in the end. Make the number of egg mayo sandwiches the  same. LCM of 1 and 11 is 11.

Number of egg mayo sandwiches 
= 42 u - 24 u - 7 u
= 11 u

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

Number of club sandwiches = 7 u + 12

7 u + 12 = 11 u
11 u - 7 u = 12
4 u = 12

1 u = 12 ÷ 4 = 4

Number of salmon sandwiches sold
= 24 u - 11 u
= 13 u
= 13 x 4
= 52

Answer(s): 52