Question

A polar bear rests by a stack of 3000 pounds of fish he has caught. He plans to travel 1000 miles across the Arctic to bring as many fish as possible to his family. He can pull a sled that holds up to 1000 pounds of fish, but he must eat 1 pound of fish at every mile to keep his energy up. What is the maximum amount of fish (in pounds) the polar bear can transport across the Arctic?
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Answer 1

The initial number of fish = 3000
Total distance to travel = 1000 miles

The bear can pull up to 1000 pounds of fish, so this is the initial pounds of fish at the beginning of the 1000-mile trip.

After every mile, the number of fish decreases by 1, so the number of fish after every successive mile is
a₀ = 1000,  to begin
a₁ = 999 = 1000 - 1   (after 1 mile)
a₂ = 998 = 1000 - 2   (after 2 miles)

Inductively, after n miles,
$a_{n} = 1000-n$

After 1000 miles,
a₁₀₀₀ = 1000 - 1000 = 0

This means that the bear starts pulling 1000 pounds of fish but eats them all up by the time it travels 1000 miles.

Answer: 1000 pounds
The maximum amount of fish the polar bear can transport. is 1000 pounds.