A convenience store sold salmon, peanut butter and bacon sandwiches. The ratio of the number of salmon sandwiches made to the total number of sandwiches made was 5 : 8. The ratio of the number of peanut butter sandwiches made to the total number of sandwiches made was 1 : 9. After the store sold some salmon sandwiches and made another 20 peanut butter sandwiches, there was an equal number of salmon, peanut butter and bacon sandwiches left. Find the number of salmon sandwiches sold.

	Salmon	Peanut Butter	Bacon	Total
Comparing salmon to total	5x9			8x9
Comparing  peanut butter to total		1x8		9x8
	45 u	8 u	19 u	72 u

	Salmon	Peanut Butter	Bacon	Total
Before	45 u	8 u	19 u	72 u
Change	- 26 u	+ 20	No change
After	1x19 = 19 u	1x19 = 19 u	1x19 = 19 u

The total number of sandwiches is the same at first. Make the total number of sandwiches the same.  LCM of 9 and 8 is 72.

Number of bacon sandwiches remains the same at first and in the end. Make the number of bacon sandwiches the  same. LCM of 1 and 19 is 19.

Number of bacon sandwiches 
= 72 u - 45 u - 8 u
= 19 u

Number of salmon, peanut butter and bacon sandwiches is the same in the end. 

Number of peanut butter sandwiches = 8 u + 20

8 u + 20 = 19 u
19 u - 8 u = 20
11 u = 20

1 u = 20 ÷ 11 = 2

Number of salmon sandwiches sold
= 45 u - 19 u
= 26 u
= 26 x 2
= 52

Answer(s): 52