A convenience store sold bacon, salmon and ham sandwiches. The ratio of the number of bacon sandwiches made to the total number of sandwiches made was 3 : 5. The ratio of the number of salmon sandwiches made to the total number of sandwiches made was 1 : 7. After the store sold some bacon sandwiches and made another 6 salmon sandwiches, there was an equal number of bacon, salmon and ham sandwiches left. Find the number of bacon sandwiches sold.

	Bacon	Salmon	Ham	Total
Comparing bacon to total	3x7			5x7
Comparing  salmon to total		1x5		7x5
	21 u	5 u	9 u	35 u

	Bacon	Salmon	Ham	Total
Before	21 u	5 u	9 u	35 u
Change	- 12 u	+ 6	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 7 and 5 is 35.

Number of ham sandwiches remains the same at first and in the end. Make the number of ham sandwiches the  same. LCM of 1 and 9 is 9.

Number of ham sandwiches 
= 35 u - 21 u - 5 u
= 9 u

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

Number of salmon sandwiches = 5 u + 6

5 u + 6 = 9 u
9 u - 5 u = 6
4 u = 6

1 u = 6 ÷ 4 = 9

Number of bacon sandwiches sold
= 21 u - 9 u
= 12 u
= 12 x 9
= 108

Answer(s): 108