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

	Salmon	Club	Ham	Total
Comparing salmon to total	5x8			9x8
Comparing  club to total		1x9		8x9
	40 u	9 u	23 u	72 u

	Salmon	Club	Ham	Total
Before	40 u	9 u	23 u	72 u
Change	- 17 u	+ 18	No change
After	1x23 = 23 u	1x23 = 23 u	1x23 = 23 u

The total number of sandwiches is the same at first. Make the total number of sandwiches the same.  LCM of 8 and 9 is 72.

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 23 is 23.

Number of ham sandwiches 
= 72 u - 40 u - 9 u
= 23 u

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

Number of club sandwiches = 9 u + 18

9 u + 18 = 23 u
23 u - 9 u = 18
14 u = 18

1 u = 18 ÷ 14 = 6

Number of salmon sandwiches sold
= 40 u - 23 u
= 17 u
= 17 x 6
= 102

Answer(s): 102