A convenience store sold tuna, bacon and chicken 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 bacon sandwiches made to the total number of sandwiches made was 1 : 7. After the store sold some tuna sandwiches and made another 11 bacon sandwiches, there was an equal number of tuna, bacon and chicken sandwiches left. Find the number of tuna sandwiches sold.

	Tuna	Bacon	Chicken	Total
Comparing tuna to total	1x7			2x7
Comparing  bacon to total		1x2		7x2
	7 u	2 u	5 u	14 u

	Tuna	Bacon	Chicken	Total
Before	7 u	2 u	5 u	14 u
Change	- 2 u	+ 11	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 chicken sandwiches remains the same at first and in the end. Make the number of chicken sandwiches the  same. LCM of 1 and 5 is 5.

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

Number of tuna, bacon and chicken sandwiches is the same in the end. 

Number of bacon sandwiches = 2 u + 11

2 u + 11 = 5 u
5 u - 2 u = 11
3 u = 11

1 u = 11 ÷ 3 = 9

Number of tuna sandwiches sold
= 7 u - 5 u
= 2 u
= 2 x 9
= 18

Answer(s): 18