A convenience store sold tuna, chicken and egg mayo sandwiches. The ratio of the number of tuna sandwiches made to the total number of sandwiches made was 4 : 7. The ratio of the number of chicken sandwiches made to the total number of sandwiches made was 1 : 6. After the store sold some tuna sandwiches and made another 6 chicken sandwiches, there was an equal number of tuna, chicken and egg mayo sandwiches left. Find the number of tuna sandwiches sold.

	Tuna	Chicken	Egg Mayo	Total
Comparing tuna to total	4x6			7x6
Comparing  chicken to total		1x7		6x7
	24 u	7 u	11 u	42 u

	Tuna	Chicken	Egg Mayo	Total
Before	24 u	7 u	11 u	42 u
Change	- 13 u	+ 6	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 6 and 7 is 42.

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 11 is 11.

Number of egg mayo sandwiches 
= 42 u - 24 u - 7 u
= 11 u

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

Number of chicken sandwiches = 7 u + 6

7 u + 6 = 11 u
11 u - 7 u = 6
4 u = 6

1 u = 6 ÷ 4 = 5

Number of tuna sandwiches sold
= 24 u - 11 u
= 13 u
= 13 x 5
= 65

Answer(s): 65