Putting
Mathematical Statements Together

Now that we've written out what we
know, we can start combining what we know to deduce the answer. This is similar
to the reasoning process that you followed in section 3.2 to deduce who Danny's
mom was, and also similar to the reasoning process that you followed to recover
the missing precipitation data in section 3.10

For example, we can
combine these two mathematical expressions:

MaximumGearWeight = 243
(TRUE).

JimGearWeight + JaneGearWeight + ScottGearWeight =
MaximumGearWeight (TRUE).

To give us another new TRUE expression. Read
over the statements a few times and try to guess what it might be.

Since
we know that the maximum gear weight is 243 pounds AND that everyone's
individual gear will add up to the maximum gear weight, we can reason that
everyone's gear will, when added up together, add up to 243 pounds.
Written using variables and symbols, that is:

JimGearWeight +
JaneGearWeight + ScottGearWeight = 243 pounds (TRUE).

Again, to put
this reasoning in words, we are saying "The maximum weight of the sled is
243 pounds, and everyone's gear has to add up to the maximum weight of the
sled, so everyone's gear has to add up to 243 pounds." This sort of
mathematical reasoning is a skill that takes practice.

We also know
from section 3.20 that

JimGearWeight = GearWeightPerPerson (TRUE)

JaneGearWeight
= GearWeightPerPerson (TRUE)

ScottGearWeight = GearWeightPerPerson (TRUE)

This
means that we if we put these equations together with the TRUE equation

JimGearWeight
+ JaneGearWeight + ScottGearWeight = 243 pounds (TRUE)

we can write a new TRUE equation:

GearWeightPerPerson
+ GearWeightPerPerson + GearWeightPerPerson = 243 pounds (TRUE).

Why?
(Answer 1)

In words this says that if we add the maximum gear weight
per person together three times, it must equal 243 pounds.

This is
useful because we've replaced three different variable names with one variable
name, that names the same number three times.

Now we are getting
closer to answering the question. We just need to find one number, which, when
added together 3 times, equals 243 pounds. To put it more abstractly, we need
something that makes the equation

x + x + x = 243 TRUE.

(Here
I've just replaced the variable name GearWeightPerPerson with the shorter
variable name 'x' to make the structure of the equation more obvious)

Can
you guess an answer now? What value of x will make this equation TRUE?

(Answer
2)

And that means that Jim, Jane and Scott can each take 81 pounds of
gear with them on the hunting trip.

Answers

Answer 1:

The
reasoning is that, if we know each person's gear is going to be equal in weight
to the same thing- GearWeightPerPerson- and we know that the weight of
everyone's gear added together is 243 pounds, then we know that
GearWeightPerPerson added together three times must also be equal to 243 pounds

Answer
2: 81

Copyright Jen Schellinck, 2006