A convenience store sold club, tuna and jam sandwiches. The ratio of the number of club sandwiches made to the total number of sandwiches made was 5 : 8. The ratio of the number of tuna sandwiches made to the total number of sandwiches made was 1 : 9. After the store sold some club sandwiches and made another 18 tuna sandwiches, there was an equal number of club, tuna and jam sandwiches left. Find the number of club sandwiches sold.

	Club	Tuna	Jam	Total
Comparing club to total	5x9			8x9
Comparing  tuna to total		1x8		9x8
	45 u	8 u	19 u	72 u

	Club	Tuna	Jam	Total
Before	45 u	8 u	19 u	72 u
Change	- 26 u	+ 18	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 9 and 8 is 72.

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 19 is 19.

Number of jam sandwiches 
= 72 u - 45 u - 8 u
= 19 u

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

Number of tuna sandwiches = 8 u + 18

8 u + 18 = 19 u
19 u - 8 u = 18
11 u = 18

1 u = 18 ÷ 11 = 3

Number of club sandwiches sold
= 45 u - 19 u
= 26 u
= 26 x 3
= 78

Answer(s): 78