A convenience store sold jam, egg mayo and club 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 : 9. After the store sold some jam sandwiches and made another 21 egg mayo sandwiches, there was an equal number of jam, egg mayo and club sandwiches left. Find the number of jam sandwiches sold.

	Jam	Egg Mayo	Club	Total
Comparing jam to total	1x9			2x9
Comparing  egg mayo to total		1x2		9x2
	9 u	2 u	7 u	18 u

	Jam	Egg Mayo	Club	Total
Before	9 u	2 u	7 u	18 u
Change	- 2 u	+ 21	No change
After	1x7 = 7 u	1x7 = 7 u	1x7 = 7 u

The total number of sandwiches is the same at first. Make the total number of sandwiches the same.  LCM of 9 and 2 is 18.

Number of club sandwiches remains the same at first and in the end. Make the number of club sandwiches the  same. LCM of 1 and 7 is 7.

Number of club sandwiches 
= 18 u - 9 u - 2 u
= 7 u

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

Number of egg mayo sandwiches = 2 u + 21

2 u + 21 = 7 u
7 u - 2 u = 21
5 u = 21

1 u = 21 ÷ 5 = 2

Number of jam sandwiches sold
= 9 u - 7 u
= 2 u
= 2 x 2
= 4

Answer(s): 4