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### Use Factoring to Find Two Consecutive Integers...

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Date: 7/31/96 at 13:52:49
From: Deena Kumar
Subject: Use Factoring to Find Two Consecutive Integers...

I am having a little trouble with using factoring in problem solving.
The instructions say to solve the problem and reject the solutions
that do not meet the conditions of the problem.The problem is as
follows:

Find two consecutive integers whose product is 56.

Here is how I tried to do it:

Let y = the smaller integer. Then let y + 1 = the larger integer.
2
y(y + 1) = 56 = y * y + y * 1 = 56 = y + y = 56

2
y + y = 56

2
y + y - 56 = 0

(y + 8)(y - 7) = 0

y + 8 = 0         y - 7 = 0

y = -8            y = 7

It is obvious that the answer is 7 and 8, but my dilemma is that; in
2
order for y + y - 56 = 0 to be true, the "y" must be a sum of a larger
positive integer (8) and a smaller negative integer (-7). I know my
method must be wrong, but it is the only way I know. How should I go
help.

D.S.K.
```

```
Date: 7/31/96 at 14:12:42
From: Doctor Robert
Subject: Re: Use Factoring to Find Two Consecutive Integers...

You have worked out the problem in the correct fashion.  I think that
you are not interpreting your results correctly.  There are two values
of y, namely 7 and -8 that will work.  If you use 7, then 7 and 8 are
the desired integers (remember you let y and y+1 be your variables).
If you use -8, then the integers are -8 and -7.  Both these solutions
integers, we would have had to reject the -8 solution. I hope that
this clears things up.

-Doctor Robert,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
Middle School Algebra

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