A convenience store sold egg mayo, bacon and tuna sandwiches. The ratio of the number of egg mayo sandwiches made to the total number of sandwiches made was 3 : 7. The ratio of the number of bacon sandwiches made to the total number of sandwiches made was 1 : 4. After the store sold some egg mayo sandwiches and made another 10 bacon sandwiches, there was an equal number of egg mayo, bacon and tuna sandwiches left. Find the number of egg mayo sandwiches sold.

	Egg Mayo	Bacon	Tuna	Total
Comparing egg mayo to total	3x4			7x4
Comparing  bacon to total		1x7		4x7
	12 u	7 u	9 u	28 u

	Egg Mayo	Bacon	Tuna	Total
Before	12 u	7 u	9 u	28 u
Change	- 3 u	+ 10	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 4 and 7 is 28.

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

Number of tuna sandwiches 
= 28 u - 12 u - 7 u
= 9 u

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

Number of bacon sandwiches = 7 u + 10

7 u + 10 = 9 u
9 u - 7 u = 10
2 u = 10

1 u = 10 ÷ 2 = 3

Number of egg mayo sandwiches sold
= 12 u - 9 u
= 3 u
= 3 x 3
= 9

Answer(s): 9