The Math Forum

Ask Dr. Math - Questions and Answers from our Archives
Associated Topics || Dr. Math Home || Search Dr. Math

Integer problem

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

        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
don't think there is an answer to your question.

Please write back if you have more questions about this or another problem.

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

Search the Dr. Math Library:

Find items containing (put spaces between keywords):
Click only once for faster results:

[ Choose "whole words" when searching for a word like age.]

all keywords, in any order at least one, that exact phrase
parts of words whole words

Submit your own question to Dr. Math

[Privacy Policy] [Terms of Use]

Math Forum Home || Math Library || Quick Reference || Math Forum Search

Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.