A convenience store sold ham, bacon and jam sandwiches. The ratio of the number of ham sandwiches made to the total number of sandwiches made was 5 : 9. The ratio of the number of bacon sandwiches made to the total number of sandwiches made was 1 : 5. After the store sold some ham sandwiches and made another 11 bacon sandwiches, there was an equal number of ham, bacon and jam sandwiches left. Find the number of ham sandwiches sold.

	Ham	Bacon	Jam	Total
Comparing ham to total	5x5			9x5
Comparing  bacon to total		1x9		5x9
	25 u	9 u	11 u	45 u

	Ham	Bacon	Jam	Total
Before	25 u	9 u	11 u	45 u
Change	- 14 u	+ 11	No change
After	1x11 = 11 u	1x11 = 11 u	1x11 = 11 u

The total number of sandwiches is the same at first. Make the total number of sandwiches the same.  LCM of 5 and 9 is 45.

Number of jam sandwiches remains the same at first and in the end. Make the number of jam sandwiches the  same. LCM of 1 and 11 is 11.

Number of jam sandwiches 
= 45 u - 25 u - 9 u
= 11 u

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

Number of bacon sandwiches = 9 u + 11

9 u + 11 = 11 u
11 u - 9 u = 11
2 u = 11

1 u = 11 ÷ 2 = 6

Number of ham sandwiches sold
= 25 u - 11 u
= 14 u
= 14 x 6
= 84

Answer(s): 84