small and big popcorn bags

Question

A large bag of popcorn is 2 1/2 of a small bag. at the end of a party there is 3 1/3 small popcorn bags and 2 1/4 large popcorn bags. How many small popcorn bags do we need for the remaining popcorn.

Answer 1

Let the volume of a big bag be V and the volume of a small bag be v. We are told that V=2.5v, that there are 3-1/3 small bags and 2-1/4 big bags left. So the total volume that is left is

3-1/3 v + 2-1/4 V. Substituting 2.5v in place of V, we get a total volume that is left is

3-1/3 v + 2-1/4 (2.5v). We can write this line as 3-1/3 v + (9/4)*(5/2)*v= 3-1/3v + (40/8)v. This sum is just

(3-1/3 + 5)v = 8-1/3v, so it takes 8-1/3 small bags to hold all the left over popcorn.