A convenience store sold bacon, egg mayo and ham sandwiches. The ratio of the number of bacon sandwiches made to the total number of sandwiches made was 3 : 5. The ratio of the number of egg mayo sandwiches made to the total number of sandwiches made was 1 : 8. After the store sold some bacon sandwiches and made another 18 egg mayo sandwiches, there was an equal number of bacon, egg mayo and ham sandwiches left. Find the number of bacon sandwiches sold.

	Bacon	Egg Mayo	Ham	Total
Comparing bacon to total	3x8			5x8
Comparing  egg mayo to total		1x5		8x5
	24 u	5 u	11 u	40 u

	Bacon	Egg Mayo	Ham	Total
Before	24 u	5 u	11 u	40 u
Change	- 13 u	+ 18	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 8 and 5 is 40.

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 11 is 11.

Number of ham sandwiches 
= 40 u - 24 u - 5 u
= 11 u

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

Number of egg mayo sandwiches = 5 u + 18

5 u + 18 = 11 u
11 u - 5 u = 18
6 u = 18

1 u = 18 ÷ 6 = 3

Number of bacon sandwiches sold
= 24 u - 11 u
= 13 u
= 13 x 3
= 39

Answer(s): 39