A convenience store sold chicken, salmon and club sandwiches. The ratio of the number of chicken sandwiches made to the total number of sandwiches made was 4 : 9. The ratio of the number of salmon sandwiches made to the total number of sandwiches made was 1 : 7. After the store sold some chicken sandwiches and made another 18 salmon sandwiches, there was an equal number of chicken, salmon and club sandwiches left. Find the number of chicken sandwiches sold.

	Chicken	Salmon	Club	Total
Comparing chicken to total	4x7			9x7
Comparing  salmon to total		1x9		7x9
	28 u	9 u	26 u	63 u

	Chicken	Salmon	Club	Total
Before	28 u	9 u	26 u	63 u
Change	- 2 u	+ 18	No change
After	1x26 = 26 u	1x26 = 26 u	1x26 = 26 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 club sandwiches remains the same at first and in the end. Make the number of club sandwiches the  same. LCM of 1 and 26 is 26.

Number of club sandwiches 
= 63 u - 28 u - 9 u
= 26 u

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

Number of salmon sandwiches = 9 u + 18

9 u + 18 = 26 u
26 u - 9 u = 18
17 u = 18

1 u = 18 ÷ 17 = 6

Number of chicken sandwiches sold
= 28 u - 26 u
= 2 u
= 2 x 6
= 12

Answer(s): 12