Splitting Peanuts

Date: 08/03/2002 at 12:23:48
From: Paul Tammaro
Subject: Math Word Problem titled DON'T FEED THE ANIMALS

On a camping trip, the Family family had brought many bags of peanuts 
for snacks. Peanuts were everyone's favorite, and so they were well 
stocked. Unfortunately, the campground was quite populated by various 
animals that also enjoyed an occasional peanut.

The first night, after the Family family went to bed, a raccoon 
visited the camp and ate five of the bags of peanuts they had brought.  
The next day, the Familys ate one-third of the remaining bags for 
breakfast. That night, a beaver came to call and ate two more of the 
bags. The next day, the Familys consumed one-fourth of the remaining 
bags for breakfast. Then they took a boat trip and they had to feed 
one bag of peanuts to each of their five dogs to get them to quiet 
down. That night, an elephant from a nearby zoo came to the camp and 
ate four bags of peanuts. The next day, each member of the Family 
family ate one-ninth of the remaining bags. That night, a spotted owl 
ate half of the remaining bags. The next day there were only four bags 
left.  The family couldn't decide how to split them amongst the five 
of them, so they fed the remaining bags of peanuts to the ducks.

How many bags of peanuts did the Family family bring with them on the 
camping trip?

Date: 08/03/2002 at 17:54:35
From: Doctor Jaffee
Subject: Re: Math Word Problem titled DON'T FEED THE ANIMALS

Hi Paul,

I can think of two good ways to solve this problem. The first is 
algebraic in nature and the second is numeric.

In the algebraic method, let x = the original number of bags of 
peanuts.  After the raccoon eats 5 bags, the number of remaining bags 
is x - 5.

Now, after the family eats 1/3 of the remaining bags, they are left 
with 2/3 of the x - 5, or (2/3)(x - 5).  Then the beaver takes 2 bags, 
so subtract 2 from the total, then multiply the result by 3/4. (If the 
family eats 1/4 of the remaining bags, they will be left with 3/4 of 
what they had).

Continue this process until you end up with a fairly nasty looking 
algebraic expression equal to 4, the number of bags of peanuts that 
were fed to the ducks. Solve that equation and you will have your 
answer.

The numeric method involves solving the problem backward. The Family 
family ended up with 4 bags of peanuts after the owl had eaten 1/2 of 
what they previously had. Since 4 x 2 = 8, there must have been 8 bags 
before the owl found them. Prior to that each of the 5 members of the 
family had eaten 1/9 of the total, leaving 4/9 of the total. So, if 
you divide 8 by 4/9, you get 18, the number of bags before each family 
member had a 1/9 share. Continue working the problem backward 
accordingly and you will eventually determine the original amount.

Give it a try and if you want to check your answer with me or if you 
are having difficulties and need more help, write back and I'll try to 
give you some assistance.

Good luck.

- Doctor Jaffee, The Math Forum
  http://mathforum.org/dr.math/