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).

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?

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