A convenience store sold egg mayo, ham and bacon 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 ham sandwiches made to the total number of sandwiches made was 1 : 9. After the store sold some egg mayo sandwiches and made another 29 ham sandwiches, there was an equal number of egg mayo, ham and bacon sandwiches left. Find the number of egg mayo sandwiches sold.

	Egg Mayo	Ham	Bacon	Total
Comparing egg mayo to total	1x9			2x9
Comparing  ham to total		1x2		9x2
	9 u	2 u	7 u	18 u

	Egg Mayo	Ham	Bacon	Total
Before	9 u	2 u	7 u	18 u
Change	- 2 u	+ 29	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 bacon sandwiches remains the same at first and in the end. Make the number of bacon sandwiches the  same. LCM of 1 and 7 is 7.

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

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

Number of ham sandwiches = 2 u + 29

2 u + 29 = 7 u
7 u - 2 u = 29
5 u = 29

1 u = 29 ÷ 5 = 2

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

Answer(s): 4