A convenience store sold club, bacon and chicken sandwiches. The ratio of the number of club 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 club sandwiches and made another 27 bacon sandwiches, there was an equal number of club, bacon and chicken sandwiches left. Find the number of club sandwiches sold.

	Club	Bacon	Chicken	Total
Comparing club to total	4x4			9x4
Comparing  bacon to total		1x9		4x9
	16 u	9 u	11 u	36 u

	Club	Bacon	Chicken	Total
Before	16 u	9 u	11 u	36 u
Change	- 5 u	+ 27	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 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 
= 36 u - 16 u - 9 u
= 11 u

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

Number of bacon sandwiches = 9 u + 27

9 u + 27 = 11 u
11 u - 9 u = 27
2 u = 27

1 u = 27 ÷ 2 = 3

Number of club sandwiches sold
= 16 u - 11 u
= 5 u
= 5 x 3
= 15

Answer(s): 15