A convenience store sold tuna, peanut butter and club sandwiches. The ratio of the number of tuna sandwiches made to the total number of sandwiches made was 1 : 2. The ratio of the number of peanut butter sandwiches made to the total number of sandwiches made was 1 : 7. After the store sold some tuna sandwiches and made another 17 peanut butter sandwiches, there was an equal number of tuna, peanut butter and club sandwiches left. Find the number of tuna sandwiches sold.

	Tuna	Peanut Butter	Club	Total
Comparing tuna to total	1x7			2x7
Comparing  peanut butter to total		1x2		7x2
	7 u	2 u	5 u	14 u

	Tuna	Peanut Butter	Club	Total
Before	7 u	2 u	5 u	14 u
Change	- 2 u	+ 17	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 club sandwiches remains the same at first and in the end. Make the number of club sandwiches the  same. LCM of 1 and 5 is 5.

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

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

Number of peanut butter sandwiches = 2 u + 17

2 u + 17 = 5 u
5 u - 2 u = 17
3 u = 17

1 u = 17 ÷ 3 = 2

Number of tuna sandwiches sold
= 7 u - 5 u
= 2 u
= 2 x 2
= 4

Answer(s): 4