Finding Numbers Using Their Product

Date: 3/24/96 at 13:29:49
From: RDIANNE GREEN
Subject: math help

Dear Doctor Math,

I am home schooled and I have been unable to answer the following 
algebra questions.

I am hoping you can help give me insight into these problems:  

1. The product of two consecutive integers is 240.  What are the 
   integers?  (Note that the product of two positive integers will 
   be positive, and that the product of two negative integers will 
   also be positive.)  "Reject roots that do not fulfill the 
   conditions of the problem."

2. A lot has an area of 4,500 square feet.  Its length is 40 feet 
   longer than its width.  What are the dimensions of the lot?

For the first question I am supposed to give the answer in the 
four step process.

Thanks a lot in advance for your help.
Hope to get your response soon,

jodi

Date: 3/24/96 at 14:11:55
From: Doctor Steven
Subject: Re: math help

Well, so as I don't actually do the work for you I'll give you 
some VERY similar problems and work through them.

#1. Say the product of two consecutive integers is 182.

    Step 1) Call the first integer x, then the second integer is 
            x+1.

    Step 2) Set up the equation given by the information, namely 
            that:

              x*(x+1) = 182.

    Step 3) Simplify to get:

              x^2 + x - 182 = 0.

    Step 4) Use quadratic equation to get:

              x = - 14, or x = 13.

    So the numbers are -14, -13, or 13, 14.

#2. Say a lot has 6000 square feet, and its length is 40 feet 
    longer than its width.

    Step 1) Call its width x, then its length is x+40.

    Step 2) Set up the equation to get:

              x*(x+40) = 6000.

    Step 3) Simplify to get:

              x^2 + 40x - 6000 = 0.

    Step 4) Use the quadratic equation to get

              x = 60, or x = -100.

Since negative lengths don't make sense, discard the -100 value, 
and you get the dimensions of this lot as 60 ft * 100 ft.

-Doctor Steven,  The Math Forum