A convenience store sold tuna, jam and egg mayo sandwiches. The ratio of the number of tuna 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 tuna sandwiches and made another 14 jam sandwiches, there was an equal number of tuna, jam and egg mayo sandwiches left. Find the number of tuna sandwiches sold.

	Tuna	Jam	Egg Mayo	Total
Comparing tuna to total	1x7			2x7
Comparing  jam to total		1x2		7x2
	7 u	2 u	5 u	14 u

	Tuna	Jam	Egg Mayo	Total
Before	7 u	2 u	5 u	14 u
Change	- 2 u	+ 14	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 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 5 is 5.

Number of egg mayo sandwiches 
= 14 u - 7 u - 2 u
= 5 u

Number of tuna, jam and egg mayo sandwiches is the same in the end. 

Number of jam sandwiches = 2 u + 14

2 u + 14 = 5 u
5 u - 2 u = 14
3 u = 14

1 u = 14 ÷ 3 = 7

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

Answer(s): 14