Cleo the Camel and the Banana Dilemma

1
Cleo the Cameland the BananaDilemma

• Clever Cleos Method
• presented by
• Mrs. Finck

2
Problem Statement

• Cleo the Camel works on a banana plantation.
  There are three thousand bananas to take to a
  market that is one thousand miles away. Cleo can
  only carry one thousand bananas at a time, and
  she must eat one banana each and every mile she
  walks.
• The Task
• What is the maximum number of bananas that
  Cleo can get to market?

3
First Attempt

• 1000 miles
• If Cleo eats one banana before she goes, she can
  carry 1000 bananas on her back, eat one banana
  each and every mile and have one banana left when
  she makes it to market. There would be 1999
  bananas left at the plantation, but Cleo could
  not go back to get them.

1
4
Second Attempt

• 500 miles 500
  miles
• If Cleo eats one banana before she goes, she can
  carry 1000 bananas on her back 500 miles, eating
  one banana each and every mile. She can go back
  for more bananas, but she has to eat 500 bananas
  on the way back. After five trips going back and
  fourth Cleo will have 503 bananas to go the next
  500 miles. She will get only two banana to
  market. There will not be any bananas left at the
  plantation.

501 -500 501 -500
2
5
Third attempt

• 250 750
• If Cleo only goes one fourth of the way, she can
  move 1250 bananas 250 miles. If she take 1000
  bananas the rest of the way, she must leave 250
  bananas behind, but she will get 250 bananas to
  market. She can not go back for the other 250
  bananas left behind.

750 -250 750 -250
250
6
Fourth Attempt

• 200 200 600
• If Cleo travels one fifth of the way, she can get
  2000 bananas at the 200 mile mark. Then if she
  travels another 200 miles, she can get 1400
  banana at the 400 mark. If she takes 1000 of
  those bananas the remaining 600 miles, she will
  bring 400 banana to market. There will be 400
  bananas left behind that she cannot go back and
  get.

800 -200 800 -200
800 -200
400
7
Fifth Attempt

• 200 333
  467
• If Cleo travels one fifth of the way, she can get
  2000 bananas at the 200 mile mark. Then if she
  travels one third of the remaining distance, she
  can get 1001 bananas at the 533 mark. If she eats
  one banana first and then takes 1000 of those
  bananas the remaining 467 miles, she will bring
  534 bananas to market. There will be no bananas
  left behind.

800 -200 800 -200
800 -200
534
8
The Math behind it!

• Five trips Three trips One trip
• 1000 5 200 First stop should be at 200
  miles, which brings 2000 bananas to that
  location.
• 1000 3 333 Second stop should be at the
  next 333 miles, which brings 1001 bananas to that
  location.
• 1001 467 534 Last stop is the market.
  There are 467 remaining miles to get to the
  market. 534 is the number of Bananas that will
  make it to market.

9
Reflection

• I love problems that make me think. In this
  problem I maximized the trips and distances in
  order to move the most amount of bananas and have
  Cleo eat the least amount of bananas. I observed
  the patterns in each attempt. This involved
  using fractions and division as well as
  subtraction and then addition. The problem
  reminded me of Drt problems even though I did
  not use this formula. I used a guess and check
  method until I could see a logical pattern. I
  then used the pattern to develop a plan to get
  the most bananas to market.

10
The End