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

	Bacon	Chicken	Peanut Butter	Total
Comparing bacon to total	5x9			8x9
Comparing  chicken to total		1x8		9x8
	45 u	8 u	19 u	72 u

	Bacon	Chicken	Peanut Butter	Total
Before	45 u	8 u	19 u	72 u
Change	- 26 u	+ 8	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 peanut butter sandwiches remains the same at first and in the end. Make the number of peanut butter sandwiches the  same. LCM of 1 and 19 is 19.

Number of peanut butter sandwiches 
= 72 u - 45 u - 8 u
= 19 u

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

Number of chicken sandwiches = 8 u + 8

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

1 u = 8 ÷ 11 = 8

Number of bacon sandwiches sold
= 45 u - 19 u
= 26 u
= 26 x 8
= 208

Answer(s): 208