Subject: word problem write up
Name: Marie Rich
Who is asking: Student
I think the answer is 533:
Corey starts with 3000 bananas.
She cannot bring more than 2000 bananas to a distance of 200 miles. Because more would involve three trips forth (and two trips back) which would cost 5 bananas on each mile, for a total of 5 bananas * 200 miles = 1000 bananas, leaving her with no more than 2000 bananas.
But she can bring 2000 bananas to a distance of 200 miles:
1st trip load 1000, eat 200, drop 600, bring back 200 for the road,
Then starting with 2000 bananas, she cannot bring more than 1001 bananas to a distance of 333 miles, because she does one trip forth, one back and one forth, so that each mile costs 3 bananas.
So Corey can get to a distance of 1000 - 200 - 333 = 467 miles of the market with 1001 bananas.
My advice is then to relax and have a banana. Then she can load the 1000 remaining bananas on her back and head to the market, and she'll have 533 bananas when she gets there. (Any other ploy would involve one trip back, hence cost a banana anyway.)