Coming up with true statements.

The next step in solving the problem is coming up with true mathematical expressions that describe the situation mathematically.

For example, we know that it's true that the maximum weight on Jim's sled is 243 pounds, so using our variable names we can create the true mathematical equation:

MaximumGearWeight = 243 pounds (TRUE).

Another true statement that we know is that the weight of everyone's gear has to add up to (no more than) the maximum weight that can go on Jim's sled. For now, we're going to assume that everyone will take the maximum weight that they can. We can write this as:

JimGearWeight + JaneGearWeight + ScottGearWeight = MaximumGearWeight (TRUE).

This says "The weight of Jim's gear plus the weight of Jane's gear plus the weight of Scott's gear will be equal to the maximum weight that Jim's sled can carry."

Since we've said that everyone will take the same weight per person, we can also write

JimGearWeight = GearWeightPerPerson (TRUE)

JaneGearWeight = GearWeightPerPerson (TRUE)

ScottGearWeight = GearWeightPerPerson (TRUE)

The first statement of these three statements says "The weight of Jim's gear will be equal to the gear weight per person that each person on the trip is allowed to take".

What do the other two statements say?

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