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### Integer problem

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Date: Wed, 30 Nov 1994 14:39:06 -0500 (EST)
From: Anthony DAuria
Subject: I have a problem for you to solve!!!!

Dear Dr. Math or one of his henchmen,

I have a good problem for you to try to solve. The problem requires
an algebraic formula and it is really easy to solve. Be careful, this
problem is very TRICKY!!!!!

Here is the problem that I would like you to solve and write back with
an answer.  Thank you for your time.  I hope that this will benefit your
studies in any way.  Thank you!

Find the largest possible 2 integers such that the larger integer is
more than 3 less than 3 times the smaller one.

HINT: No guessing or trial or error is involved.

Anthony D'Auria
```

```
Date: Wed, 30 Nov 1994 19:06:40 -0500
From: Dr. Math (Margaret Patterson)
Subject: Anthony's question

Hi Anthony -

Thanks for writing to us.  My name is Margaret and I am one of the
Doctors Math.  The other doctors are other women and men at Swarthmore
College.

I couldn't tell from your question whether or not you have already
solved this problem or if it is just for our enrichment.  We only answer
questions that you need help with, not ones that you already understand.

Well, this is going to be tricky,  first notice that there are many
possible pairs of numbers for which the larger is more than3 less than 3
times the smaller one.

let x and y be the numbers you are looking for.  Let x > y.

Then we know that x > 3y-3  or x > 3(y-1)

Some possibilities are  x=10, y=2  or x=100, y=30, or even x = 1000 y=300

But, you have asked for the largest possible numbers for which this is true.
I afraid there is no limit to how big the numbers can be.  The only
constraint is that y be about 1/3 of x.  But x could be any number - so I

-Margaret Patterson, Math Doctor on call
```
Associated Topics:
Middle School Word Problems

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