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### 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

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

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/
```
Associated Topics:
Middle School Equations
Middle School Fractions
Middle School Word Problems

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