Garden Areas

Date: 8/14/96 at 13:51:21
From: Anonymous
Subject: Algebra Word Problems

Dear Dr. Math, 

I am an English teacher you have helped before. I hope you can help me 
again. I am on the chapter involving factoring and the zero product 
property. Here is a word problem with which I am having a difficult 
time:

One year, Josef put in a rectangular garden, with its length 5 feet 
more than its width. The next year, he increased the length by 3 feet 
and decreased the width by 2 feet. If the area of the second garden 
was 119 sq. feet, was the second garden larger or smaller?

Date: 8/14/96 at 22:57:59
From: Doctor Robert
Subject: Algebra Word Problems

Label the dimensions of the FIRST garden, x and x+5, where x is the 
width and x+5 is the length. 

Now, according to the problem, the SECOND garden must have a length of  
x+8 and a width of x-2. So we have the following equation:

           (x+8)(x-2) = 119

 -->     x^2 + 6x -16 = 119

 -->   x^2 + 6x - 135 = 0

 -->      (x+15)(x-9) = 0

Therefore, x = -15 or x = 9. We reject the negative value because 
though it satisfies the equation, it does not apply to our problem. 
The answer is x = 9. So the FIRST garden must have measured 14 by 9 
and the SECOND garden 7 by 17. The first garden is bigger.

Cheers.

-Doctor Robert,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/