A convenience store sold ham, salmon and chicken sandwiches. The ratio of the number of ham sandwiches made to the total number of sandwiches made was 3 : 7. The ratio of the number of salmon sandwiches made to the total number of sandwiches made was 1 : 4. After the store sold some ham sandwiches and made another 27 salmon sandwiches, there was an equal number of ham, salmon and chicken sandwiches left. Find the number of ham sandwiches sold.

	Ham	Salmon	Chicken	Total
Comparing ham to total	3x4			7x4
Comparing  salmon to total		1x7		4x7
	12 u	7 u	9 u	28 u

	Ham	Salmon	Chicken	Total
Before	12 u	7 u	9 u	28 u
Change	- 3 u	+ 27	No change
After	1x9 = 9 u	1x9 = 9 u	1x9 = 9 u

The total number of sandwiches is the same at first. Make the total number of sandwiches the same.  LCM of 4 and 7 is 28.

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 9 is 9.

Number of chicken sandwiches 
= 28 u - 12 u - 7 u
= 9 u

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

Number of salmon sandwiches = 7 u + 27

7 u + 27 = 9 u
9 u - 7 u = 27
2 u = 27

1 u = 27 ÷ 2 = 4

Number of ham sandwiches sold
= 12 u - 9 u
= 3 u
= 3 x 4
= 12

Answer(s): 12