Cutting Sheets of Paper

**DINOCALC09** · May 19th 2008, 04:12 AM

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

**Soroban** · May 19th 2008, 04:35 AM

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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