A convenience store sold jam, tuna and chicken sandwiches. The ratio of the number of jam 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 jam sandwiches and made another 28 tuna sandwiches, there was an equal number of jam, tuna and chicken sandwiches left. Find the number of jam sandwiches sold.

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

	Jam	Tuna	Chicken	Total
Before	45 u	8 u	19 u	72 u
Change	- 26 u	+ 28	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 chicken sandwiches remains the same at first and in the end. Make the number of chicken sandwiches the  same. LCM of 1 and 19 is 19.

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

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

Number of tuna sandwiches = 8 u + 28

8 u + 28 = 19 u
19 u - 8 u = 28
11 u = 28

1 u = 28 ÷ 11 = 3

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

Answer(s): 78