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 5 : 8. The ratio of the number of bacon sandwiches made to the total number of sandwiches made was 1 : 7. After the store sold some egg mayo sandwiches and made another 5 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	5x7			8x7
Comparing  bacon to total		1x8		7x8
	35 u	8 u	13 u	56 u

	Egg Mayo	Bacon	Tuna	Total
Before	35 u	8 u	13 u	56 u
Change	- 22 u	+ 5	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 tuna sandwiches remains the same at first and in the end. Make the number of tuna sandwiches the  same. LCM of 1 and 13 is 13.

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

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

Number of bacon sandwiches = 8 u + 5

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

1 u = 5 ÷ 5 = 6

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

Answer(s): 132