[etgryphon]

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(1) A bat and a ball cost $1.10 in total. The bat costs a dollar more than the ball. How much does the ball cost?


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This is the easy one using straight alegebra with no ambiguity.

x + (x + 1) = 1.10
x = 0.5

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(2) If it takes 5 machines 5 minutes to make 5 widgets, how long would it take 100 machines to make 100 widgets?


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The true answer to this is a system of solutions because there is ambiguity introduced with the terms "5 machines" it does not explicitly state that these are "identical" machines with the same production rate so there is techinically an infinite number of solutions.

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(3) In a lake, there is a patch of lily pads. Every day, the patch doubles in size. If it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half of the lake?


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This is easy if we use day unit measurements because when the "exact" time that the lily pads cover half the lake is dependent on the initial size of the lily patch at the exponentally preportional size of the lake to that initial size of the lily patch.

But it will always cross the "half lake threshold" T-1 in unit days where T = the whole lake being covered.

-Gryph