A convenience store sold chicken, club and egg mayo sandwiches. The ratio of the number of chicken sandwiches made to the total number of sandwiches made was 5 : 9. The ratio of the number of club sandwiches made to the total number of sandwiches made was 1 : 7. After the store sold some chicken sandwiches and made another 14 club sandwiches, there was an equal number of chicken, club and egg mayo sandwiches left. Find the number of chicken sandwiches sold.

	Chicken	Club	Egg Mayo	Total
Comparing chicken to total	5x7			9x7
Comparing  club to total		1x9		7x9
	35 u	9 u	19 u	63 u

	Chicken	Club	Egg Mayo	Total
Before	35 u	9 u	19 u	63 u
Change	- 16 u	+ 14	No change
After	1x19 = 19 u	1x19 = 19 u	1x19 = 19 u

The total number of sandwiches is the same at first. Make the total number of sandwiches the same.  LCM of 7 and 9 is 63.

Number of egg mayo sandwiches remains the same at first and in the end. Make the number of egg mayo sandwiches the  same. LCM of 1 and 19 is 19.

Number of egg mayo sandwiches 
= 63 u - 35 u - 9 u
= 19 u

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

Number of club sandwiches = 9 u + 14

9 u + 14 = 19 u
19 u - 9 u = 14
10 u = 14

1 u = 14 ÷ 10 = 2

Number of chicken sandwiches sold
= 35 u - 19 u
= 16 u
= 16 x 2
= 32

Answer(s): 32