Question 189449
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Let <i>x</i> be the number of plants that he starts with, just like you said.  Now, if he gives the first guard half <i><b>plus</b></i> 2, what he will have left is half <i><b>minus</b></i> 2.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  \frac{x}{2}-2]


And this is the amount he will have when he gives the next guard half plus 2; after which encounter he will have:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  \frac{\frac{x}{2}-2}{2}-2]


remaining.  And finally, after the last encounter he has:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  \frac{\frac{\frac{x}{2}-2}{2}-2}{2}-2]


remaining, and we are told this is equal to 1, so:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  \frac{\frac{\frac{x}{2}-2}{2}-2}{2}-2 = 1]


Add 2 to both sides, then multiply by 2.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  \frac{\frac{x}{2}-2}{2}-2 = 6]


Add 2 to both sides, then multiply by 2.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  \frac{x}{2}-2= 16]


Add 2 to both sides, then multiply by 2.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  x = 36]





John
*[tex \LARGE e^{i\pi} + 1 = 0]
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