A convenience store sold chicken, peanut butter and bacon sandwiches. The ratio of the number of chicken sandwiches made to the total number of sandwiches made was 1 : 2. 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 chicken sandwiches and made another 24 peanut butter sandwiches, there was an equal number of chicken, peanut butter and bacon sandwiches left. Find the number of chicken sandwiches sold.

	Chicken	Peanut Butter	Bacon	Total
Comparing chicken to total	1x9			2x9
Comparing  peanut butter to total		1x2		9x2
	9 u	2 u	7 u	18 u

	Chicken	Peanut Butter	Bacon	Total
Before	9 u	2 u	7 u	18 u
Change	- 2 u	+ 24	No change
After	1x7 = 7 u	1x7 = 7 u	1x7 = 7 u

The total number of sandwiches is the same at first. Make the total number of sandwiches the same.  LCM of 9 and 2 is 18.

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 7 is 7.

Number of bacon sandwiches 
= 18 u - 9 u - 2 u
= 7 u

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

Number of peanut butter sandwiches = 2 u + 24

2 u + 24 = 7 u
7 u - 2 u = 24
5 u = 24

1 u = 24 ÷ 5 = 7

Number of chicken sandwiches sold
= 9 u - 7 u
= 2 u
= 2 x 7
= 14

Answer(s): 14