How Many Pads of Paper?

Date: 10/30/2001 at 02:23:05
From: Jessica
Subject: Number Theory

A merchant marked some pads of paper down from $2.00 and sold the 
entire lot. If the gross profit from the sale was $603.77, how many 
pads did he sell?

I don't understand how to solve this without knowing at least one more 
variable, like how much or what percent they were marked down to.

Date: 10/30/2001 at 08:46:16
From: Doctor Paul
Subject: Re: Number Theory

The integer 60377 has only four factors: 1, 173, 349, 60377

So 60377 = 1 * 60377 or 173 * 349

It follows then that 

   603.77 =  .01 * 60377   or 
            1.73 * 349     or 
             173 * 3.49    or 
               1 * 603.77

But since we know the merchant charged less than $2.00, we can assume 
he sold them for either $1.73 each or $.01 each.

In the former case he sold 349 pads, and in the latter case he sold 
60377 pads.

Notice that 1.73 * 349 = 603.7699999999999999999999999...  and 
.01 * 60377 = 603.77

I'm guessing that the correct answer here is probably 349 since the 
other case is obvious and wouldn't require you to do much work. But if 
the problem is stated exactly as you have it written above, 60377 
would be a legitimate answer as well.

Feel free to write back if you want to talk about this some more.

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