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

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

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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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?)

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?)

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