A convenience store sold ham, peanut butter and chicken sandwiches. The ratio of the number of ham sandwiches made to the total number of sandwiches made was 4 : 9. The ratio of the number of peanut butter sandwiches made to the total number of sandwiches made was 1 : 5. After the store sold some ham sandwiches and made another 24 peanut butter sandwiches, there was an equal number of ham, peanut butter and chicken sandwiches left. Find the number of ham sandwiches sold.

	Ham	Peanut Butter	Chicken	Total
Comparing ham to total	4x5			9x5
Comparing  peanut butter to total		1x9		5x9
	20 u	9 u	16 u	45 u

	Ham	Peanut Butter	Chicken	Total
Before	20 u	9 u	16 u	45 u
Change	- 4 u	+ 24	No change
After	1x16 = 16 u	1x16 = 16 u	1x16 = 16 u

The total number of sandwiches is the same at first. Make the total number of sandwiches the same.  LCM of 5 and 9 is 45.

Number of chicken sandwiches remains the same at first and in the end. Make the number of chicken sandwiches the  same. LCM of 1 and 16 is 16.

Number of chicken sandwiches 
= 45 u - 20 u - 9 u
= 16 u

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

Number of peanut butter sandwiches = 9 u + 24

9 u + 24 = 16 u
16 u - 9 u = 24
7 u = 24

1 u = 24 ÷ 7 = 7

Number of ham sandwiches sold
= 20 u - 16 u
= 4 u
= 4 x 7
= 28

Answer(s): 28