$\textbf{Camel and Bananas}$
Joe, the owner of a banana farm, has a camel. He wants to transport his $3000$ bananas to the market which is located at the other side of the desert. The distance between his banana farm and the market is $1000$ kilometers. The camel can carry at most $1000$ bananas at a time, and also eats one banana for every kilometer traveled. What is the maximum number of bananas Joe can bring to the market?
$\textbf{Answer}$
$533$.
$\textbf{Analysis}$
As the camel can carry at most $1000$ bananas at a time and currently there are $3000$ bananas, it will take the camel three trips to move all the bananas to somewhere along the road. Our first goal is to find how far we can go in this first stage so we can have $2000$ bananas remaining. This will then allow us to reduce the number of trips to two in the next stage.
From the starting point, it will take $5$ one-way journeys to complete the three required trips (go to the staging point, return to the origin, go to the staging point, return to the origin, and go to the staging point). Assume the distance we can travel is $x$, then we have the following relation because for each kilometer traveled, the camel needs to eat one banana: $$5x = 3000-2000\implies x=200$$
Now, in the second stage, Joe need to have three one-way journeys to move these $2000$ bananas as far as possible and leave $1000$ remaining for the final adventure. Assume the distance traveled in this stage is $y$, then $$3y=2000-1000\implies y \approx 333.3$$
By now, Joe and the camel have traveled $200+333.3 =533.3$ kilometers and have $1000$ bananas left. The remaining distance is $1000-533.3=466.7$ kilometers which will cost $467$ bananas (Joe cannot sell a partially eaten banana). This leaves the $533$ bananas available for sell at the market.