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Math Help - Cutting Sheets of Paper

  1. #1
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    Lightbulb Cutting Sheets of Paper

    Alejando cuts sheets of paper to make ballots.

    1 cut = 2 Ballots
    2 cut = 4 Ballots
    3 cut = 8 Ballots
    4 cut = 16 Ballots
    5 cut = 32 Ballots
    AND SO ON...

    From this you can get the equation: y=2^n

    Say that a stack of 250 sheets of paper is 1 inch high. How high would a stack of ballots be after 20 cuts?

    How many cuts would Alejandro need to make to have a stack of ballots 1 foot high?

    Thanks
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  2. #2
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    Hello, DINOCALC09!

    This is mostly Arithmetic . . . Exactly where is your difficulty?


    Alejando cuts sheets of paper to make ballots.

    1 cut = 2 Ballots
    2 cut = 4 Ballots
    3 cut = 8 Ballots
    4 cut = 16 Ballots
    5 cut = 32 Ballots
    . . and so on ...

    From this you can get the equation: . y\:=\:2^n

    (a) Say that a stack of 250 sheets of paper is 1 inch high.
    How high would a stack of ballots be after 20 cuts?

    After 20 cuts, there are: . 2^{20} \:=:1,048,576 ballots.

    At 250 to an inch, the stack is: . \frac{1,048,576}{250} \:\approx\:4194\text{ inches} \:\approx\:349.5\text{ feet high}



    (b) How many cuts would Alejandro need to make to have a stack of ballots 1 foot high?

    \text{1 foot} \:=\:12\text{ inches} \:=\:3000\text{ ballots}


    We have: . 2^n \:\geq \:3000

    Take logs: . \ln(2^n) \:\geq\:\ln(3000) \quad\Rightarrow\quad n\cdot\ln(2) \:\geq\:\ln(3000)

    Hence: . n \;\geq\;\frac{\ln(3000)}{\ln(2)} \;=\;11.55074679

    Therefore, he must make 12 cuts.

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