Consecutive Integers

Date: 11/7/95 at 21:9:43
From: Anonymous
Subject: 9th Grade Math - Consecutive Integer Problems

Problem #1 - 

Write 4 consecutive even integers beginning with each of the 
following integers:

                 26
                -20

Problem #2 -  

Find two consecutive even integers such that twice the smaller is 
26 less than three times the larger.

Problem #3 -

Is it possible to find 3 consecutive odd integers whose sum is 59?  
Why?
        
Need Help!  Thanks.

Leah Ouellette 
(age 14, Indian River High School, Philadelphia, New York)

Date: 11/12/95 at 16:17:35
From: Doctor Ethan
Subject: Re: 9th Grade Math - Consecutive Integer Problems

Hello Leah,

Let's think together.  What does it mean to say that we have 
consecutive numbers?

Are 3,7,14,75 consecutive?

Are 3,4,5,6,7?

In hope you said no to the first list and yes to the second.
The first list does not have a particular order.  The second goes 
from one number to the next to the next.

So when we ask for consecutive even numbers we mean a list that 
starts at some even number like 8 then goes to the next one 10 and 
then the next one 12 and then 14,16,18,... You get the idea.  Or 
if we started with -8 the next one would be -6 because we always 
go up.

[if you can use a number line then a good approach is to start at 
a point and then take the next number to the right that is what 
you want(ie odd or even depending on the problem.)]

Does this help you with number one?

Now what I will do is get you started with number two and then 
maybe that will show you how to do number 3 as well.

We want two consecutive even integers such that twice the smaller 
is 26 less than 3 times the larger.

Okay if we call the smaller x then what is the large one going to 
be? If they are consecutive even integers (like 4 and 6) then the 
big one is two greater than the small one so call it x + 2

small = x
big = x+2

Then what is "twice the smaller"?  That is just 2x.  And "26 less 
than 3 times the larger" is 3(x+2) - 26 

[if you don't see how I got these then ask somebody or write back 
to us]

So because of the "is" in "twice the smaller is 26 less than 3 
times the larger." we can set these things equal to one another 
and then solve for x.

That is 2x = 3(x+2) - 26.

Can you get it from here?  If not then write back for more help.

-Doctor Ethan,  The Geometry Forum