A convenience store sold salmon, jam and club 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 jam sandwiches made to the total number of sandwiches made was 1 : 7. After the store sold some salmon sandwiches and made another 25 jam sandwiches, there was an equal number of salmon, jam and club sandwiches left. Find the number of salmon sandwiches sold.

	Salmon	Jam	Club	Total
Comparing salmon to total	1x7			2x7
Comparing  jam to total		1x2		7x2
	7 u	2 u	5 u	14 u

	Salmon	Jam	Club	Total
Before	7 u	2 u	5 u	14 u
Change	- 2 u	+ 25	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 club sandwiches remains the same at first and in the end. Make the number of club sandwiches the  same. LCM of 1 and 5 is 5.

Number of club sandwiches 
= 14 u - 7 u - 2 u
= 5 u

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

Number of jam sandwiches = 2 u + 25

2 u + 25 = 5 u
5 u - 2 u = 25
3 u = 25

1 u = 25 ÷ 3 = 7

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

Answer(s): 14