A convenience store sold tuna, chicken and ham sandwiches. The ratio of the number of tuna sandwiches made to the total number of sandwiches made was 5 : 8. The ratio of the number of chicken sandwiches made to the total number of sandwiches made was 1 : 7. After the store sold some tuna sandwiches and made another 30 chicken sandwiches, there was an equal number of tuna, chicken and ham sandwiches left. Find the number of tuna sandwiches sold.

	Tuna	Chicken	Ham	Total
Comparing tuna to total	5x7			8x7
Comparing  chicken to total		1x8		7x8
	35 u	8 u	13 u	56 u

	Tuna	Chicken	Ham	Total
Before	35 u	8 u	13 u	56 u
Change	- 22 u	+ 30	No change
After	1x13 = 13 u	1x13 = 13 u	1x13 = 13 u

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

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 13 is 13.

Number of ham sandwiches 
= 56 u - 35 u - 8 u
= 13 u

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

Number of chicken sandwiches = 8 u + 30

8 u + 30 = 13 u
13 u - 8 u = 30
5 u = 30

1 u = 30 ÷ 5 = 6

Number of tuna sandwiches sold
= 35 u - 13 u
= 22 u
= 22 x 6
= 132

Answer(s): 132