A convenience store sold jam, egg mayo and chicken sandwiches. The ratio of the number of jam sandwiches made to the total number of sandwiches made was 3 : 5. The ratio of the number of egg mayo sandwiches made to the total number of sandwiches made was 1 : 9. After the store sold some jam sandwiches and made another 6 egg mayo sandwiches, there was an equal number of jam, egg mayo and chicken sandwiches left. Find the number of jam sandwiches sold.

	Jam	Egg Mayo	Chicken	Total
Comparing jam to total	3x9			5x9
Comparing  egg mayo to total		1x5		9x5
	27 u	5 u	13 u	45 u

	Jam	Egg Mayo	Chicken	Total
Before	27 u	5 u	13 u	45 u
Change	- 14 u	+ 6	No change
After	1x13 = 13 u	1x13 = 13 u	1x13 = 13 u

The total number of sandwiches is the same at first. Make the total number of sandwiches the same.  LCM of 9 and 5 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 13 is 13.

Number of chicken sandwiches 
= 45 u - 27 u - 5 u
= 13 u

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

Number of egg mayo sandwiches = 5 u + 6

5 u + 6 = 13 u
13 u - 5 u = 6
8 u = 6

1 u = 6 ÷ 8 = 4

Number of jam sandwiches sold
= 27 u - 13 u
= 14 u
= 14 x 4
= 56

Answer(s): 56