A convenience store sold chicken, bacon and salmon sandwiches. The ratio of the number of chicken 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 chicken sandwiches and made another 5 bacon sandwiches, there was an equal number of chicken, bacon and salmon sandwiches left. Find the number of chicken sandwiches sold.

	Chicken	Bacon	Salmon	Total
Comparing chicken to total	5x7			8x7
Comparing  bacon to total		1x8		7x8
	35 u	8 u	13 u	56 u

	Chicken	Bacon	Salmon	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 salmon sandwiches remains the same at first and in the end. Make the number of salmon sandwiches the  same. LCM of 1 and 13 is 13.

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

Number of chicken, bacon and salmon 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 = 2

Number of chicken sandwiches sold
= 35 u - 13 u
= 22 u
= 22 x 2
= 44

Answer(s): 44