A Real World
Example of Using Equations

Suppose that Jim, Jane and Scott are going
out hunting for a week. On the way back from the trip, Jane and Scott are going
to put the animals they have caught on their skidoos and Jim is going to put
all of their hunting gear, food and other gear on his skidoo. They know that
each person's gear should weigh about the same amount as everyone else's gear.
Jim also knows that his skidoo can easily handle about 243 pounds of gear
weight. They need to figure out how much gear each person can bring on the
trip.

Can you already guess or figure out how much gear each person
can bring without creating a mathematical description? What do you think the
answer is?

Now suppose you want to find the answer mathematically by
creating a mathematical description for this real world problem.

Usually,
the first thing to do when creating a mathematical description of a real world
problem is to figure out what facts or information you already know, and what
information you don't yet know but might want to know.

What facts do
we know already? List them in point form

(Answer 1)

What facts
don't we know? List them in point form

(Answer 2)

Now we need
to decide which of these facts is actually relevant to the particular question
we are trying to answer at this moment, which is: "How much gear can each
person bring on the trip, if it all has to fit on Jim's skidoo?"

There
are certainly other questions we could ask, like "Will everyone be able to
bring enough gear if Jim's sled can only carry 243 pounds?" and "How
much gas do we need to bring for a long trip?" but these are separate
questions. For now we are only considering the question: "How much gear
can each person bring on the trip, if it all has to fit on Jim's skidoo".

In
this case, not all of the facts we listed above will necessarily be relevant to
the problem at hand. Often it's useful to guess which facts are particularly
relevant to the problem, although it may turn out that others become relevant
as the problem progresses.

In this case, relevant facts or information
we know might be:

Jim's skidoo is going to carry
all the gear on the way back

Jim's sled can take 243 pounds

Relevant
facts or information we don't know, but need to solve this particular problem
might be:

The number of pounds of gear Jim can take

the number of
pounds of gear Jane can take

the number of pounds of gear Scott can take.

The
next step in the problem is to create some variable names. We'll consider this
step in secction 3.19

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Answer 1: A possible answer

Facts
or information we know

Jim, Jane and Scott are going out for a week.

There
are three skidoos

Two of the skidoos are going to be used for animals on
the way back

Jim's skidoo is going to carry the gear

Jim's sled can
take 243 pounds.

We have 3 people going on the trip.

Everyone can take
the same amount of gear.

(Anything else?)

Answer 2: A possible
answer

Facts or information we don't know

The number of
pounds of gear Jim can take

the number of pounds of gear Jane can take

the
number of pounds of gear Scott can take.

How much meat Jim, Jane and Scott
will be taking backing.

How far the skidoos can drive without running out
of gas.

(Anything else?)

Copyright Jen Schellinck, 2006