A convenience store sold egg mayo, chicken and ham sandwiches. The ratio of the number of egg mayo sandwiches made to the total number of sandwiches made was 2 : 3. The ratio of the number of chicken sandwiches made to the total number of sandwiches made was 1 : 8. After the store sold some egg mayo sandwiches and made another 14 chicken sandwiches, there was an equal number of egg mayo, chicken and ham sandwiches left. Find the number of egg mayo sandwiches sold.

	Egg Mayo	Chicken	Ham	Total
Comparing egg mayo to total	2x8			3x8
Comparing  chicken to total		1x3		8x3
	16 u	3 u	5 u	24 u

	Egg Mayo	Chicken	Ham	Total
Before	16 u	3 u	5 u	24 u
Change	- 11 u	+ 14	No change
After	1x5 = 5 u	1x5 = 5 u	1x5 = 5 u

The total number of sandwiches is the same at first. Make the total number of sandwiches the same.  LCM of 8 and 3 is 24.

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 5 is 5.

Number of ham sandwiches 
= 24 u - 16 u - 3 u
= 5 u

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

Number of chicken sandwiches = 3 u + 14

3 u + 14 = 5 u
5 u - 3 u = 14
2 u = 14

1 u = 14 ÷ 2 = 5

Number of egg mayo sandwiches sold
= 16 u - 5 u
= 11 u
= 11 x 5
= 55

Answer(s): 55