A convenience store sold bacon, ham and club 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 : 9. After the store sold some bacon sandwiches and made another 26 ham sandwiches, there was an equal number of bacon, ham and club sandwiches left. Find the number of bacon sandwiches sold.

	Bacon	Ham	Club	Total
Comparing bacon to total	1x9			2x9
Comparing  ham to total		1x2		9x2
	9 u	2 u	7 u	18 u

	Bacon	Ham	Club	Total
Before	9 u	2 u	7 u	18 u
Change	- 2 u	+ 26	No change
After	1x7 = 7 u	1x7 = 7 u	1x7 = 7 u

The total number of sandwiches is the same at first. Make the total number of sandwiches the same.  LCM of 9 and 2 is 18.

Number of club sandwiches remains the same at first and in the end. Make the number of club sandwiches the  same. LCM of 1 and 7 is 7.

Number of club sandwiches 
= 18 u - 9 u - 2 u
= 7 u

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

Number of ham sandwiches = 2 u + 26

2 u + 26 = 7 u
7 u - 2 u = 26
5 u = 26

1 u = 26 ÷ 5 = 2

Number of bacon sandwiches sold
= 9 u - 7 u
= 2 u
= 2 x 2
= 4

Answer(s): 4