A convenience store sold jam, bacon and tuna sandwiches. The ratio of the number of jam sandwiches made to the total number of sandwiches made was 2 : 3. The ratio of the number of bacon sandwiches made to the total number of sandwiches made was 1 : 8. After the store sold some jam sandwiches and made another 22 bacon sandwiches, there was an equal number of jam, bacon and tuna sandwiches left. Find the number of jam sandwiches sold.

	Jam	Bacon	Tuna	Total
Comparing jam to total	2x8			3x8
Comparing  bacon to total		1x3		8x3
	16 u	3 u	5 u	24 u

	Jam	Bacon	Tuna	Total
Before	16 u	3 u	5 u	24 u
Change	- 11 u	+ 22	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 8 and 3 is 24.

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 5 is 5.

Number of tuna sandwiches 
= 24 u - 16 u - 3 u
= 5 u

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

Number of bacon sandwiches = 3 u + 22

3 u + 22 = 5 u
5 u - 3 u = 22
2 u = 22

1 u = 22 ÷ 2 = 9

Number of jam sandwiches sold
= 16 u - 5 u
= 11 u
= 11 x 9
= 99

Answer(s): 99