Which is More?

Date: 05/21/2002 at 20:02:55
From: bridget
Subject: money

You are offered a choice of nickels stacked on top of each other to 
equal your height, or quarters placed side by side to equal your 
height. Which would you choose and why? 

I tried several different ways to get this answer but I'm not good 
with numbers and I can't figure out the anwser.  Please help me.  

Thank you,
Bridget

Date: 05/21/2002 at 20:38:24
From: Doctor Ian
Subject: Re: money

Hi Bridget,

Let's pretend for a moment that your height is exactly the same 
as the diameter of a quarter.  Now the problem is easier, isn't 
it? 

You just have to stand a quarter on its edge, stack some nickels 
up until they reach the top, and see whether the nickels add up 
to more than 25 cents.  

If they add up to more than 25 cents, you would choose the 
nickels. Otherwise, you'd choose the quarter.   Does that make 
sense?

Now, suppose you're TWO quarters high, instead of just one.  Or 
three quarters high.  Or five, or six, or seven, or any number of 
quarters high.  Would there be any reason to make a different 
choice? 

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/