#### How good is your mathematical intuition on this problem?

I was thinking about what should be about as simple a math problem as possible. You have two boxes A and B loaded with packages. Box A weighs 10 pounds more than box B. You would like the boxes to be closer in weight. You pick up packages a from A and b from B and consider swapping them.

It was not immediately obvious to me how to analyze this situation. Without writing any equations, do the answers to the following questions come to you immediately, or do you have to give it some thought?

Is it obvious that you can determine what the difference in weight between A and B will be based on the difference in weights between a and b?

What will happen if a weighs less than b?

What happens if a is 0 to 5 pounds heavier than b?

What about if a is 5 to 10 pounds heavier than b?

Finally, what if a is more than 10 pounds heavier than b?

Write an equation using and b for what the difference in weight between the two boxes will be if the packages are swapped. Express as succinctly as possible what the weight difference between a and b must be in order for the weight difference between A and B to be reduced by swapping a and b.

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