A convenience store sold jam, egg mayo and ham sandwiches. The ratio of the number of jam sandwiches made to the total number of sandwiches made was 1 : 2. The ratio of the number of egg mayo sandwiches made to the total number of sandwiches made was 1 : 7. After the store sold some jam sandwiches and made another 7 egg mayo sandwiches, there was an equal number of jam, egg mayo and ham sandwiches left. Find the number of jam sandwiches sold.

	Jam	Egg Mayo	Ham	Total
Comparing jam to total	1x7			2x7
Comparing  egg mayo to total		1x2		7x2
	7 u	2 u	5 u	14 u

	Jam	Egg Mayo	Ham	Total
Before	7 u	2 u	5 u	14 u
Change	- 2 u	+ 7	No change
After	1x5 = 5 u	1x5 = 5 u	1x5 = 5 u

The total number of sandwiches is the same at first. Make the total number of sandwiches the same.  LCM of 7 and 2 is 14.

Number of ham sandwiches remains the same at first and in the end. Make the number of ham sandwiches the  same. LCM of 1 and 5 is 5.

Number of ham sandwiches 
= 14 u - 7 u - 2 u
= 5 u

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

Number of egg mayo sandwiches = 2 u + 7

2 u + 7 = 5 u
5 u - 2 u = 7
3 u = 7

1 u = 7 ÷ 3 = 2

Number of jam sandwiches sold
= 7 u - 5 u
= 2 u
= 2 x 2
= 4

Answer(s): 4