A convenience store sold ham, bacon and peanut butter sandwiches. The ratio of the number of ham sandwiches made to the total number of sandwiches made was 5 : 7. The ratio of the number of bacon sandwiches made to the total number of sandwiches made was 1 : 9. After the store sold some ham sandwiches and made another 18 bacon sandwiches, there was an equal number of ham, bacon and peanut butter sandwiches left. Find the number of ham sandwiches sold.

	Ham	Bacon	Peanut Butter	Total
Comparing ham to total	5x9			7x9
Comparing  bacon to total		1x7		9x7
	45 u	7 u	11 u	63 u

	Ham	Bacon	Peanut Butter	Total
Before	45 u	7 u	11 u	63 u
Change	- 34 u	+ 18	No change
After	1x11 = 11 u	1x11 = 11 u	1x11 = 11 u

The total number of sandwiches is the same at first. Make the total number of sandwiches the same.  LCM of 9 and 7 is 63.

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 11 is 11.

Number of peanut butter sandwiches 
= 63 u - 45 u - 7 u
= 11 u

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

Number of bacon sandwiches = 7 u + 18

7 u + 18 = 11 u
11 u - 7 u = 18
4 u = 18

1 u = 18 ÷ 4 = 4

Number of ham sandwiches sold
= 45 u - 11 u
= 34 u
= 34 x 4
= 136

Answer(s): 136