A convenience store sold egg mayo, bacon and jam sandwiches. The ratio of the number of egg mayo sandwiches made to the total number of sandwiches made was 1 : 2. The ratio of the number of bacon sandwiches made to the total number of sandwiches made was 1 : 7. After the store sold some egg mayo sandwiches and made another 9 bacon sandwiches, there was an equal number of egg mayo, bacon and jam sandwiches left. Find the number of egg mayo sandwiches sold.

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

	Egg Mayo	Bacon	Jam	Total
Before	7 u	2 u	5 u	14 u
Change	- 2 u	+ 9	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 jam sandwiches remains the same at first and in the end. Make the number of jam sandwiches the  same. LCM of 1 and 5 is 5.

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

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

Number of bacon sandwiches = 2 u + 9

2 u + 9 = 5 u
5 u - 2 u = 9
3 u = 9

1 u = 9 ÷ 3 = 4

Number of egg mayo sandwiches sold
= 7 u - 5 u
= 2 u
= 2 x 4
= 8

Answer(s): 8