A convenience store sold chicken, egg mayo and bacon sandwiches. The ratio of the number of chicken sandwiches made to the total number of sandwiches made was 4 : 9. The ratio of the number of egg mayo sandwiches made to the total number of sandwiches made was 1 : 4. After the store sold some chicken sandwiches and made another 21 egg mayo sandwiches, there was an equal number of chicken, egg mayo and bacon sandwiches left. Find the number of chicken sandwiches sold.

	Chicken	Egg Mayo	Bacon	Total
Comparing chicken to total	4x4			9x4
Comparing  egg mayo to total		1x9		4x9
	16 u	9 u	11 u	36 u

	Chicken	Egg Mayo	Bacon	Total
Before	16 u	9 u	11 u	36 u
Change	- 5 u	+ 21	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 bacon sandwiches remains the same at first and in the end. Make the number of bacon sandwiches the  same. LCM of 1 and 11 is 11.

Number of bacon sandwiches 
= 36 u - 16 u - 9 u
= 11 u

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

Number of egg mayo sandwiches = 9 u + 21

9 u + 21 = 11 u
11 u - 9 u = 21
2 u = 21

1 u = 21 ÷ 2 = 8

Number of chicken sandwiches sold
= 16 u - 11 u
= 5 u
= 5 x 8
= 40

Answer(s): 40