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

	Ham	Egg Mayo	Salmon	Total
Comparing ham to total	1x7			2x7
Comparing  egg mayo to total		1x2		7x2
	7 u	2 u	5 u	14 u

	Ham	Egg Mayo	Salmon	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 salmon sandwiches remains the same at first and in the end. Make the number of salmon sandwiches the  same. LCM of 1 and 5 is 5.

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

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

Number of egg mayo sandwiches = 2 u + 14

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

1 u = 14 ÷ 3 = 8

Number of ham sandwiches sold
= 7 u - 5 u
= 2 u
= 2 x 8
= 16

Answer(s): 16