A convenience store sold tuna, egg mayo and salmon sandwiches. The ratio of the number of tuna sandwiches made to the total number of sandwiches made was 3 : 5. The ratio of the number of egg mayo sandwiches made to the total number of sandwiches made was 1 : 7. After the store sold some tuna sandwiches and made another 20 egg mayo sandwiches, there was an equal number of tuna, egg mayo and salmon sandwiches left. Find the number of tuna sandwiches sold.

	Tuna	Egg Mayo	Salmon	Total
Comparing tuna to total	3x7			5x7
Comparing  egg mayo to total		1x5		7x5
	21 u	5 u	9 u	35 u

	Tuna	Egg Mayo	Salmon	Total
Before	21 u	5 u	9 u	35 u
Change	- 12 u	+ 20	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 7 and 5 is 35.

Number of salmon sandwiches remains the same at first and in the end. Make the number of salmon sandwiches the  same. LCM of 1 and 9 is 9.

Number of salmon sandwiches 
= 35 u - 21 u - 5 u
= 9 u

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

Number of egg mayo sandwiches = 5 u + 20

5 u + 20 = 9 u
9 u - 5 u = 20
4 u = 20

1 u = 20 ÷ 4 = 3

Number of tuna sandwiches sold
= 21 u - 9 u
= 12 u
= 12 x 3
= 36

Answer(s): 36