A convenience store sold jam, chicken and tuna sandwiches. The ratio of the number of jam sandwiches made to the total number of sandwiches made was 5 : 7. The ratio of the number of chicken sandwiches made to the total number of sandwiches made was 1 : 8. After the store sold some jam sandwiches and made another 18 chicken sandwiches, there was an equal number of jam, chicken and tuna sandwiches left. Find the number of jam sandwiches sold.

	Jam	Chicken	Tuna	Total
Comparing jam to total	5x8			7x8
Comparing  chicken to total		1x7		8x7
	40 u	7 u	9 u	56 u

	Jam	Chicken	Tuna	Total
Before	40 u	7 u	9 u	56 u
Change	- 31 u	+ 18	No change
After	1x9 = 9 u	1x9 = 9 u	1x9 = 9 u

The total number of sandwiches is the same at first. Make the total number of sandwiches the same.  LCM of 8 and 7 is 56.

Number of tuna sandwiches remains the same at first and in the end. Make the number of tuna sandwiches the  same. LCM of 1 and 9 is 9.

Number of tuna sandwiches 
= 56 u - 40 u - 7 u
= 9 u

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

Number of chicken sandwiches = 7 u + 18

7 u + 18 = 9 u
9 u - 7 u = 18
2 u = 18

1 u = 18 ÷ 2 = 5

Number of jam sandwiches sold
= 40 u - 9 u
= 31 u
= 31 x 5
= 155

Answer(s): 155