A convenience store sold club, jam and tuna 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 jam sandwiches made to the total number of sandwiches made was 1 : 8. After the store sold some club sandwiches and made another 14 jam sandwiches, there was an equal number of club, jam and tuna sandwiches left. Find the number of club sandwiches sold.

	Club	Jam	Tuna	Total
Comparing club to total	4x8			7x8
Comparing  jam to total		1x7		8x7
	32 u	7 u	17 u	56 u

	Club	Jam	Tuna	Total
Before	32 u	7 u	17 u	56 u
Change	- 15 u	+ 14	No change
After	1x17 = 17 u	1x17 = 17 u	1x17 = 17 u

The total number of sandwiches is the same at first. Make the total number of sandwiches the same.  LCM of 8 and 7 is 56.

Number of tuna sandwiches remains the same at first and in the end. Make the number of tuna sandwiches the  same. LCM of 1 and 17 is 17.

Number of tuna sandwiches 
= 56 u - 32 u - 7 u
= 17 u

Number of club, jam and tuna sandwiches is the same in the end. 

Number of jam sandwiches = 7 u + 14

7 u + 14 = 17 u
17 u - 7 u = 14
10 u = 14

1 u = 14 ÷ 10 = 6

Number of club sandwiches sold
= 32 u - 17 u
= 15 u
= 15 x 6
= 90

Answer(s): 90