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

	Bacon	Club	Chicken	Total
Comparing bacon to total	3x8			5x8
Comparing  club to total		1x5		8x5
	24 u	5 u	11 u	40 u

	Bacon	Club	Chicken	Total
Before	24 u	5 u	11 u	40 u
Change	- 13 u	+ 9	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 chicken sandwiches remains the same at first and in the end. Make the number of chicken sandwiches the  same. LCM of 1 and 11 is 11.

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

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

Number of club sandwiches = 5 u + 9

5 u + 9 = 11 u
11 u - 5 u = 9
6 u = 9

1 u = 9 ÷ 6 = 6

Number of bacon sandwiches sold
= 24 u - 11 u
= 13 u
= 13 x 6
= 78

Answer(s): 78