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Math Help - Elimination by Addition Method / Word Problem

  1. #1
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    Elimination by Addition Method / Word Problem

    I'm working on this section in my Algebra book called Elimination by Addition Method/Systems using two linear equations and I'm stuck on this word problem.
    Can somebody please help me and explain how to set it up and solve it?
    Thanks.

    Suppose that we have a rectangular book cover. If the width is increased by 2 centimeters, and the length is decreased by 1 centimeter, then the area is increased by 28 square centimeters. However, if the width is decreased by 1 centimeter and the length is increased by 2 centimeters, then the area is increased by 10 square centimeters. Find the dimensions of the book cover.

    This is what I tried doing

    (W+2)(L-1)= 28
    (W-1)(L+2)=10

    I know I'm doing something wrong and I cant figure out another way to set up the equations.
    Last edited by dcarranza; May 11th 2012 at 04:12 AM.
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  2. #2
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    Re: Elimination by Addition Method / Word Problem

    Quote Originally Posted by dcarranza View Post
    Suppose that we have a rectangular book cover. If the width is increased by 2 centimeters, and the length is decreased by 1 centimeter, then the area is increased by 28 square centimeters. However, if the width is decreased by 1 centimeter and the length is increased by 2 centimeters, then the area is increased by 10 square centimeters. Find the dimensions of the book cover.

    This is what I tried doing

    (W+2)(L-1)= 28
    (W-1)(L+2)=10
    You're showing the increases of 28 and 10 as new areas;
    they really are increases to the original area of WL; so :
    (W + 2)(L - 1) = WL + 28 [1]
    (W - 1)(L + 2) = WL + 10 [2]

    Now expand the left sides:
    WL - W + 2L - 2 = WL + 28 [1]
    WL + 2W - L - 2 = WL + 10 [2]

    Simplify:
    -W + 2L = 30 [1]
    2W - L = 12 [2]

    I'll leave you the satisfaction of finishing that up
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  3. #3
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    Re: Elimination by Addition Method / Word Problem

    I finally solved it! Thank you so much!
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