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### 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

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

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.

- Doctor Paul, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Middle School Factoring Numbers
Middle School Word Problems

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