A convenience store sold ham, salmon and tuna sandwiches. The ratio of the number of ham sandwiches made to the total number of sandwiches made was 1 : 2. The ratio of the number of salmon sandwiches made to the total number of sandwiches made was 1 : 7. After the store sold some ham sandwiches and made another 14 salmon sandwiches, there was an equal number of ham, salmon and tuna sandwiches left. Find the number of ham sandwiches sold.

	Ham	Salmon	Tuna	Total
Comparing ham to total	1x7			2x7
Comparing  salmon to total		1x2		7x2
	7 u	2 u	5 u	14 u

	Ham	Salmon	Tuna	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 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 ham, salmon and tuna sandwiches is the same in the end. 

Number of salmon sandwiches = 2 u + 14

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

1 u = 14 ÷ 3 = 9

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

Answer(s): 18