A convenience store sold egg mayo, ham and peanut butter sandwiches. The ratio of the number of egg mayo sandwiches made to the total number of sandwiches made was 2 : 3. The ratio of the number of ham sandwiches made to the total number of sandwiches made was 1 : 8. After the store sold some egg mayo sandwiches and made another 7 ham sandwiches, there was an equal number of egg mayo, ham and peanut butter sandwiches left. Find the number of egg mayo sandwiches sold.

	Egg Mayo	Ham	Peanut Butter	Total
Comparing egg mayo to total	2x8			3x8
Comparing  ham to total		1x3		8x3
	16 u	3 u	5 u	24 u

	Egg Mayo	Ham	Peanut Butter	Total
Before	16 u	3 u	5 u	24 u
Change	- 11 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 8 and 3 is 24.

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

Number of peanut butter sandwiches 
= 24 u - 16 u - 3 u
= 5 u

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

Number of ham sandwiches = 3 u + 7

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

1 u = 7 ÷ 2 = 7

Number of egg mayo sandwiches sold
= 16 u - 5 u
= 11 u
= 11 x 7
= 77

Answer(s): 77