A convenience store sold egg mayo, salmon and chicken sandwiches. The ratio of the number of egg mayo 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 : 5. After the store sold some egg mayo sandwiches and made another 18 salmon sandwiches, there was an equal number of egg mayo, salmon and chicken sandwiches left. Find the number of egg mayo sandwiches sold.

	Egg Mayo	Salmon	Chicken	Total
Comparing egg mayo to total	4x5			9x5
Comparing  salmon to total		1x9		5x9
	20 u	9 u	16 u	45 u

	Egg Mayo	Salmon	Chicken	Total
Before	20 u	9 u	16 u	45 u
Change	- 4 u	+ 18	No change
After	1x16 = 16 u	1x16 = 16 u	1x16 = 16 u

The total number of sandwiches is the same at first. Make the total number of sandwiches the same.  LCM of 5 and 9 is 45.

Number of chicken sandwiches remains the same at first and in the end. Make the number of chicken sandwiches the  same. LCM of 1 and 16 is 16.

Number of chicken sandwiches 
= 45 u - 20 u - 9 u
= 16 u

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

Number of salmon sandwiches = 9 u + 18

9 u + 18 = 16 u
16 u - 9 u = 18
7 u = 18

1 u = 18 ÷ 7 = 2

Number of egg mayo sandwiches sold
= 20 u - 16 u
= 4 u
= 4 x 2
= 8

Answer(s): 8