A convenience store sold club, salmon and ham sandwiches. The ratio of the number of club sandwiches made to the total number of sandwiches made was 4 : 7. The ratio of the number of salmon sandwiches made to the total number of sandwiches made was 1 : 9. After the store sold some club sandwiches and made another 14 salmon sandwiches, there was an equal number of club, salmon and ham sandwiches left. Find the number of club sandwiches sold.

	Club	Salmon	Ham	Total
Comparing club to total	4x9			7x9
Comparing  salmon to total		1x7		9x7
	36 u	7 u	20 u	63 u

	Club	Salmon	Ham	Total
Before	36 u	7 u	20 u	63 u
Change	- 16 u	+ 14	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 ham sandwiches remains the same at first and in the end. Make the number of ham sandwiches the  same. LCM of 1 and 20 is 20.

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

Number of club, salmon and ham sandwiches is the same in the end. 

Number of salmon sandwiches = 7 u + 14

7 u + 14 = 20 u
20 u - 7 u = 14
13 u = 14

1 u = 14 ÷ 13 = 7

Number of club sandwiches sold
= 36 u - 20 u
= 16 u
= 16 x 7
= 112

Answer(s): 112