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Math Help - Quadratic word problems with Geometry. Help!!

  1. #1
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    Quadratic word problems with Geometry. Help!!

    "A picture frame is 12 inches by 10 inches. If the picture that is showing in the frame is 80 square inches, and the frame is the same width on all sides, what are the dimensions of the picture?"

    Ahh where do I even start here? So far I got this:

    F(frame) = 120 in
    P(picture) = 80 in

    What do I even do here? I'm not sure!
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    Re: Quadratic word problems with Geometry. Help!!

    Call the distance between the edge of the frame and the edge of the picture 'x'. The picture's length is now 12-2x and the width 10-2x. Therefore the product of these two are 80.

    Solve for x.
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    Re: Quadratic word problems with Geometry. Help!!

    Quote Originally Posted by pickslides View Post
    Call the distance between the edge of the frame and the edge of the picture 'x'. The picture's length is now 12-2x and the width 10-2x. Therefore the product of these two are 80.

    Solve for x.
    You are a legend. I wish I could give you a 2 thankses lol!
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    Re: Quadratic word problems with Geometry. Help!!

    Quote Originally Posted by pickslides View Post
    Call the distance between the edge of the frame and the edge of the picture 'x'. The picture's length is now 12-2x and the width 10-2x. Therefore the product of these two are 80.

    Solve for x.
    Ok one question again (sorry for this.)

    So when I'm solving for X I should start my equation off like this?

    12- 2x + 10 - 2x = 80

    I have I feeling I'm doing it wrong.

    edit:

    or instead of the above equation maybe this one?

    22 - 4x = 80
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    Re: Quadratic word problems with Geometry. Help!!

    Okay, so I know what I did above ^ is wrong, because I got the answer -14.5, and a negative won't be an answer for this equation..

    Anyone help? Thank you!
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    Re: Quadratic word problems with Geometry. Help!!

    I said the product of the 2 in my post, multiply them together!

    (12-2x)(10-2x) = 80
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    Re: Quadratic word problems with Geometry. Help!!

    Quote Originally Posted by pickslides View Post
    I said the product of the 2 in my post, multiply them together!

    (12-2x)(10-2x) = 80
    Okay so got this!

    (12-2x)(10-x2)= 80

    120-40x+4x^2= 80

    -40x+4x^2=-40

    not sure what to do after this? Sorry, math is obviously not my strong point :x
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    Re: Quadratic word problems with Geometry. Help!!

    Quote Originally Posted by WannaBSmart View Post
    Okay so got this!

    (12-2x)(10-x2)= 80
    It's (12-2x)(10-2x)= 80

    120 -24x-20x +4x^2= 80

    120 -44x +4x^2= 80

    40 -44x +4x^2= 0

    4(10 -11x +x^2)= 0

    10 -11x +x^2= 0

    x^2-11x+10=0

    You can factor it from here?
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    Re: Quadratic word problems with Geometry. Help!!

    You have:

    (12-2x)(10-2x)=80

    Divide through by 4 first to make things easier!

    \frac{12-2x}{2}\cdot\frac{10-2x}{2}=\frac{80}{4}

    (6-x)(5-x)=20

    30-11x+x^2=20

    Now what you want to do is arrange in standard quadratic form:

    x^2-11x+10=0

    Now factor...can you think of two factors of 10 whose sum is -11?

    You will get two roots, but only 1 will make sense in the context of the problem.
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