A convenience store sold ham, chicken and egg mayo sandwiches. The ratio of the number of ham sandwiches made to the total number of sandwiches made was 5 : 7. The ratio of the number of chicken sandwiches made to the total number of sandwiches made was 1 : 8. After the store sold some ham sandwiches and made another 14 chicken sandwiches, there was an equal number of ham, chicken and egg mayo sandwiches left. Find the number of ham sandwiches sold.

	Ham	Chicken	Egg Mayo	Total
Comparing ham to total	5x8			7x8
Comparing  chicken to total		1x7		8x7
	40 u	7 u	9 u	56 u

	Ham	Chicken	Egg Mayo	Total
Before	40 u	7 u	9 u	56 u
Change	- 31 u	+ 14	No change
After	1x9 = 9 u	1x9 = 9 u	1x9 = 9 u

The total number of sandwiches is the same at first. Make the total number of sandwiches the same.  LCM of 8 and 7 is 56.

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 9 is 9.

Number of egg mayo sandwiches 
= 56 u - 40 u - 7 u
= 9 u

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

Number of chicken sandwiches = 7 u + 14

7 u + 14 = 9 u
9 u - 7 u = 14
2 u = 14

1 u = 14 ÷ 2 = 3

Number of ham sandwiches sold
= 40 u - 9 u
= 31 u
= 31 x 3
= 93

Answer(s): 93