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Math Help - Need help please!

  1. #1
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    Need help please!

    Heres the question:

    Two boys agree to mow a rectangular lawn 80m by 60m, each mowing half. The first boy mows a strip of uniform width around the outside of the lawn. how wide is the strip?

    So far ive figured out that each boy mows half the area which is 2400m^2, and ive wrote out an equation of the area which is length=2400/width. Now im completely stuck, can someone please help me?
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  2. #2
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    Quote Originally Posted by sugar_babee
    Heres the question:

    Two boys agree to mow a rectangular lawn 80m by 60m, each mowing half. The first boy mows a strip of uniform width around the outside of the lawn. how wide is the strip?

    So far ive figured out that each boy mows half the area which is 2400m^2, and ive wrote out an equation of the area which is length=2400/width. Now im completely stuck, can someone please help me?
    This is what you have,
    Rectange 60x80 if the width of the strip around is x then the area needs to be 2400 (half). The area of the smaller rectangle inside is
    (60-2x)(80-2x)=2400
    Then, divide by 4
    (30-x)(40-x)=600
    Thus,
    x^2-70x+1200=600
    Thus,
    x^2-70x+600=0
    Thus,
    (x-10)(x-60)=0
    Thus,
    x=10,60
    It cannot be 60 because that is too much. Thus the width of strip of 10 meters.
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  3. #3
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    Thank you so much, i get what i was missing before
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by sugar_babee
    Heres the question:

    Two boys agree to mow a rectangular lawn 80m by 60m, each mowing half. The first boy mows a strip of uniform width around the outside of the lawn. how wide is the strip?

    So far ive figured out that each boy mows half the area which is 2400m^2, and ive wrote out an equation of the area which is length=2400/width. Now im completely stuck, can someone please help me?
    Ugh. I really need to get some sort of picture drawing software!

    Imagine your rectangle. I'm taking the 80 m to be the horizontal side, which I am going to call the width. One boy is mowing a strip of uniform width around the yard. So say that he mows a strip of width x. The dimensions of the rectangle of lawn left over in the center are going to be: width = 80-2x and length = 60-2x. (There's a strip of size x on EACH side of the lawn, hence the 2x instead of x.)

    We know that the interior has an area of 2400 m^2. So
    (80-2x)(60-2x)=2400

    Solve this equation for x and you are done.
    (80-2x)(60-2x)=4x^2-280x+4800=2400
    4x^2-280x+2400=0
    and thus x = 10 m or x = 60 m using your favorite method of solution.

    I hope it's obvious that the 60 m measurement is unphysical. Thus the solution is x = 10 m.

    -Dan
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  5. #5
    Forum Admin topsquark's Avatar
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    Is there an echo in here?

    -Dan
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  6. #6
    Site Founder MathGuru's Avatar
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    is there an echo in here?
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