How Old at $4,000?

Date: 10/15/2002 at 17:48:57
From: Stephen
Subject: Word Problem

Aunt Isabella sends money to each niece and nephew on his or her 
birthday. She gives each child $10.00 on his or her first birthday.On 
each birthday thereafter, you and your cousins get $20.00 more than 
on the birthday before. How old will you be when you receive a total 
of $4,000.00 from Aunt Isabella?

Date: 10/15/2002 at 20:12:33
From: Doctor Ian
Subject: Re: Word Problem

Hi Stephen,

Instead of thinking about dollars, let's think about $10 bills. She 
gives you 1 of them on your first birthday, 3 the next one, 5 the next 
one, and so on. 

Suppose you save them, and use a magic marker to mark each one with 
the number of the birthday when you got it. Then you lay them out on a 
table like this:

   [1] [2] [3] [4]

   [2] [2] [3] [4]

   [3] [3] [3] [4]

   [4] [4] [4] [4]

Do you see how each birthday adds one more 'layer' to the square? 
 
How big would the square have to get for you to have 400 ten-dollar 
bills (which is the same as $4000)? How many years would it take to 
get that big? 

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