A convenience store sold bacon, chicken and ham sandwiches. The ratio of the number of bacon sandwiches made to the total number of sandwiches made was 5 : 9. The ratio of the number of chicken sandwiches made to the total number of sandwiches made was 1 : 7. After the store sold some bacon sandwiches and made another 25 chicken sandwiches, there was an equal number of bacon, chicken and ham sandwiches left. Find the number of bacon sandwiches sold.

	Bacon	Chicken	Ham	Total
Comparing bacon to total	5x7			9x7
Comparing  chicken to total		1x9		7x9
	35 u	9 u	19 u	63 u

	Bacon	Chicken	Ham	Total
Before	35 u	9 u	19 u	63 u
Change	- 16 u	+ 25	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 7 and 9 is 63.

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

Number of ham sandwiches 
= 63 u - 35 u - 9 u
= 19 u

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

Number of chicken sandwiches = 9 u + 25

9 u + 25 = 19 u
19 u - 9 u = 25
10 u = 25

1 u = 25 ÷ 10 = 7

Number of bacon sandwiches sold
= 35 u - 19 u
= 16 u
= 16 x 7
= 112

Answer(s): 112