A convenience store sold bacon, ham and egg mayo sandwiches. The ratio of the number of bacon sandwiches made to the total number of sandwiches made was 1 : 2. The ratio of the number of ham sandwiches made to the total number of sandwiches made was 1 : 7. After the store sold some bacon sandwiches and made another 9 ham sandwiches, there was an equal number of bacon, ham and egg mayo sandwiches left. Find the number of bacon sandwiches sold.

	Bacon	Ham	Egg Mayo	Total
Comparing bacon to total	1x7			2x7
Comparing  ham to total		1x2		7x2
	7 u	2 u	5 u	14 u

	Bacon	Ham	Egg Mayo	Total
Before	7 u	2 u	5 u	14 u
Change	- 2 u	+ 9	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 egg mayo sandwiches remains the same at first and in the end. Make the number of egg mayo sandwiches the  same. LCM of 1 and 5 is 5.

Number of egg mayo sandwiches 
= 14 u - 7 u - 2 u
= 5 u

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

Number of ham sandwiches = 2 u + 9

2 u + 9 = 5 u
5 u - 2 u = 9
3 u = 9

1 u = 9 ÷ 3 = 8

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

Answer(s): 16