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LostInParadise's avatar

Is this a good problem for first year algebra?

Asked by LostInParadise (31917points) February 4th, 2020

It is difficult to find problems that are not too difficult but still have some intrinsic interest. There are a number of good recreational math river crossing problems, which provide the motivation for this algebra problem, which requires a little reasoning but is not that difficult.

Suppose we have n > 1 people who want to cross a river. They have one boat, which can hold 2 people and requires only one person to operate. How many crossings, in either direction, must the boat make to transport all n people across the river. Anyone having difficulty solving this problem can plot points and find the equation of the line joining them.

Slightly more difficult would be to count the number of crossings required using a boat that can hold 3 people and requires one person to operate. For this problem assume n > 2 and is an odd number.

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