A convenience store sold bacon, club and ham sandwiches. The ratio of the number of bacon sandwiches made to the total number of sandwiches made was 2 : 3. The ratio of the number of club sandwiches made to the total number of sandwiches made was 1 : 8. After the store sold some bacon sandwiches and made another 21 club sandwiches, there was an equal number of bacon, club and ham sandwiches left. Find the number of bacon sandwiches sold.

	Bacon	Club	Ham	Total
Comparing bacon to total	2x8			3x8
Comparing  club to total		1x3		8x3
	16 u	3 u	5 u	24 u

	Bacon	Club	Ham	Total
Before	16 u	3 u	5 u	24 u
Change	- 11 u	+ 21	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 ham sandwiches remains the same at first and in the end. Make the number of ham sandwiches the  same. LCM of 1 and 5 is 5.

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

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

Number of club sandwiches = 3 u + 21

3 u + 21 = 5 u
5 u - 3 u = 21
2 u = 21

1 u = 21 ÷ 2 = 8

Number of bacon sandwiches sold
= 16 u - 5 u
= 11 u
= 11 x 8
= 88

Answer(s): 88