Garden AreasDate: 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/ |
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