Suppose we have a bottle with $1$L of ketchup and another bottle with 1L of mustard. We take $1$Tbsp of ketchup from the ketchup bottle and put it in the mustard bottle and then mix it (but it might not be mixed very well). Then, I take $1$Tbsp of the mixture back into the ketchup bottle. What is true about the fraction of ketchup in the ketchup bottle compared to the fraction of mustard in the mustard bottle?
I am really not sure what to do here. The problem seems so simple but I don't even know how to start.
Give names to the quantities involved. After you are finished mixing, the ketchup bottle contains a large quantity $K$ of ketchup and a small quantity $m$ of mustard, and the mustard bottle contains a large quantity $M$ of mustard and a small quantity $k$ of ketchup. What can you say about the four sums $K+m$, $M+k$, $K+k$, and $M+m$? What does this imply about the four quantities $K,k,M,m$?