SOLUTION: Cory has 3000 bananas. Cory has a camel that can carry 1000 bananas at a time. Cory's camel eats 1 banana every mile he travels. How many bananas can Cory get to the market?

Question 335123: Cory has 3000 bananas. Cory has a camel that can carry 1000 bananas at a time. Cory's camel eats 1 banana every mile he travels. How many bananas can Cory get to the market?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
Given:
Cory has 3000 bananas.
Cory has a camel that can carry 1000 bananas at a time.
Cory's camel eats 1 banana for every mile the camel travels.

Assumption:

The camel has to get to market and the camel has to get back from market.

Analysis.

The camel consumes 1 banana for every mile the camel travels.

The distance is x miles (unknown at this time).

the camel will have to make 3 trips because there are 3000 bananas and the
camel can only carry 1000 bananas each trip.

Each trip the camel travels x miles to get to the market and x miles to get
back.

That means that each trip, the camel travels 2 * x miles.

For 3 trips, that means the camel travels 3 * (2 * x) = 6 * x miles.

Since the camel consumes 1 banana for every mile that the camel travels,
this means that the camel will consume 6 * x bananas in total.

What can be sold at market are the bananas that the camel has not consumed.

Since there are 3000 bananas in total, and the camel will have to travel 6 *
x miles in total, then the number of bananas that can be sold at market is:

3000 - 6*x

If the distance to market is 100 miles, this means that 3000 - 600 = 2400
bananas can be sold as market.

This works out as follows:

First trip:

Camel gets loaded with 1000 bananas.
Camel consumes 100 bananas to get to market.
There are 900 bananas left.
Camel needs an additional 100 bananas to get back home.
There are 800 bananas left that can be sold.

This happens 3 times.

Total number of bananas that can be sold is 3 * 800 = 2400.

A major assumption is that the camel has to get to market and back and that
the camel eats 100 bananas every mile.

Change this assumption and the answer changes.

Before we change this assumption, let's assume the distance is 1000 miles.

what happens then?

the formula states that the number of bananas that can be sold at market is
given by the equation 3000 - 6*x.

If x equals 1000, then it is clear that there are not enough bananas because
3000 - 6000 = -3000.

The maximum distance would be 500 miles and no bananas would be left to
sell, because 3000 - 500*6 = 3000 - 3000 = 0.

Now let's change the assumption.

Let's assume that the camel eats 1 banana each mile that the camel takes to
get to market, but that on the return trip the camel eats something else,
just not bananas.

The formula then becomes:

Number of bananas that can be sold at market is 3000 - 3 * x.

That's 3 trips to market at x miles each trip.

Now assume that the distance is 100 miles.

You get 3000 - 3*100 = 3000 - 300 = 2700 bananas that can be sold at market.

If the distance is 500 miles, you get 3000 - 3 * 500 = 3000 - 1500 = 1500
bananas that can be sold at market.

If the distance is 1000 miles, you get 3000 - 3 * 1000 = 0 bananas that can
be sold at market.

The camel has ate them all.

At 1000 miles, under the assumption that the camel only consumes 1 banana
each mile getting to market, and consumes no bananas on the return trip from
market, you get:

First trip:

Camel is loaded with 1000 bananas.
Camel eats 1 banana for every mile camel travels to market.
After 1000 miles, camel has consumed 1000 bananas.
There are no bananas left to sell at market.

This happens for each of 3 trips, assuming the banana seller is dumb enough
to make the additional 2 trips after finding out that he has no bananas to
sell.

I suspect the problem makes the second assumption.

That is that the camel consumes 1 banana for each mile of travel going to
market only.

The answer, under that assumption, is that 0 bananas can be sold at market
because the camel has consumed them all, assuming the distance is 1000 miles.

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