A convenience store sold peanut butter, ham and club sandwiches. The ratio of the number of peanut butter sandwiches made to the total number of sandwiches made was 3 : 7. The ratio of the number of ham sandwiches made to the total number of sandwiches made was 1 : 5. After the store sold some peanut butter sandwiches and made another 11 ham sandwiches, there was an equal number of peanut butter, ham and club sandwiches left. Find the number of peanut butter sandwiches sold.

	Peanut Butter	Ham	Club	Total
Comparing peanut butter to total	3x5			7x5
Comparing  ham to total		1x7		5x7
	15 u	7 u	13 u	35 u

	Peanut Butter	Ham	Club	Total
Before	15 u	7 u	13 u	35 u
Change	- 2 u	+ 11	No change
After	1x13 = 13 u	1x13 = 13 u	1x13 = 13 u

The total number of sandwiches is the same at first. Make the total number of sandwiches the same.  LCM of 5 and 7 is 35.

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 13 is 13.

Number of club sandwiches 
= 35 u - 15 u - 7 u
= 13 u

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

Number of ham sandwiches = 7 u + 11

7 u + 11 = 13 u
13 u - 7 u = 11
6 u = 11

1 u = 11 ÷ 6 = 4

Number of peanut butter sandwiches sold
= 15 u - 13 u
= 2 u
= 2 x 4
= 8

Answer(s): 8