A convenience store sold ham, bacon and tuna sandwiches. The ratio of the number of ham sandwiches made to the total number of sandwiches made was 4 : 9. The ratio of the number of bacon sandwiches made to the total number of sandwiches made was 1 : 4. After the store sold some ham sandwiches and made another 8 bacon sandwiches, there was an equal number of ham, bacon and tuna sandwiches left. Find the number of ham sandwiches sold.

	Ham	Bacon	Tuna	Total
Comparing ham to total	4x4			9x4
Comparing  bacon to total		1x9		4x9
	16 u	9 u	11 u	36 u

	Ham	Bacon	Tuna	Total
Before	16 u	9 u	11 u	36 u
Change	- 5 u	+ 8	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 4 and 9 is 36.

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

Number of tuna sandwiches 
= 36 u - 16 u - 9 u
= 11 u

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

Number of bacon sandwiches = 9 u + 8

9 u + 8 = 11 u
11 u - 9 u = 8
2 u = 8

1 u = 8 ÷ 2 = 5

Number of ham sandwiches sold
= 16 u - 11 u
= 5 u
= 5 x 5
= 25

Answer(s): 25