A convenience store sold ham, chicken and jam sandwiches. The ratio of the number of ham sandwiches made to the total number of sandwiches made was 4 : 7. The ratio of the number of chicken sandwiches made to the total number of sandwiches made was 1 : 9. After the store sold some ham sandwiches and made another 6 chicken sandwiches, there was an equal number of ham, chicken and jam sandwiches left. Find the number of ham sandwiches sold.

	Ham	Chicken	Jam	Total
Comparing ham to total	4x9			7x9
Comparing  chicken to total		1x7		9x7
	36 u	7 u	20 u	63 u

	Ham	Chicken	Jam	Total
Before	36 u	7 u	20 u	63 u
Change	- 16 u	+ 6	No change
After	1x20 = 20 u	1x20 = 20 u	1x20 = 20 u

The total number of sandwiches is the same at first. Make the total number of sandwiches the same.  LCM of 9 and 7 is 63.

Number of jam sandwiches remains the same at first and in the end. Make the number of jam sandwiches the  same. LCM of 1 and 20 is 20.

Number of jam sandwiches 
= 63 u - 36 u - 7 u
= 20 u

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

Number of chicken sandwiches = 7 u + 6

7 u + 6 = 20 u
20 u - 7 u = 6
13 u = 6

1 u = 6 ÷ 13 = 4

Number of ham sandwiches sold
= 36 u - 20 u
= 16 u
= 16 x 4
= 64

Answer(s): 64