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Homework Help: Quadratic homework

  1. Mar 20, 2005 #1
    I was given a bunch of quadratic homework and I'm stuck on a few problems:

    "Brendan buys a black of shares for $1895. When the share price goes up by $4/share, he sells all but 15 of them for $1740. How many shares did he buy?"

    I got the equation [tex]\frac{1895}{x} - \frac{1740}{x + 4} = 15[/tex] but I worked it out and I don't get the answer (~73).

    --

    "A rectangular field has a perimeter 500 m and an area 14 400 m^2. Find the lengths of its sides."

    [tex]l * w = 14 400[/tex]
    [tex]2l + 2w = 500[/tex]
    Not sure what to do from here...

    --

    Thanks in advance for any help
     
    Last edited by a moderator: Mar 20, 2005
  2. jcsd
  3. Mar 20, 2005 #2

    arildno

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    How on earth did you get your first equation??
    It is, as far as I can see, totally wrong.

    Let "P" be the initial price for one share, and "x" the number of shares originally bought.
    Then, the information given can be written as:
    P*x=1895
    (P+4)*(x-15)=1740

    We therefore have [tex]P=\frac{1895}{x}[/tex]
    This yields a quadratic in x you can solve.
     
  4. Mar 20, 2005 #3

    t!m

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    And the second problem you have set up right and is now simply solving a system of linear equations. Solve one of the eqns for one variable ... substitute ... sound familiar?
     
  5. Mar 20, 2005 #4
    Yeah, I had worked it out like that earlier and didn't get the right answer, but I realize now it was just a dumb mistake.

    There is one last part of a question I can't get:

    "Given [itex]kx^2+(k+3)x+(3-4k) = 0[/itex]. Find the value of k if
    c) one of the roots is 2"

    Thanks for your help, both of you.
     
    Last edited by a moderator: Mar 20, 2005
  6. Mar 20, 2005 #5

    HallsofIvy

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    Notice that in the first equation you gave:[tex]\frac{1895}{x} - \frac{1740}{x + 4} = 15[/tex], The numerator of each fraction on the left is an amount of money: dollars, while the denominator is the number of shares bought: each fraction is "dollars per share".

    Actually, that's not quite correct because I assume you got the "4" from "$4/share" and you can't add "shares" to "dollars per share". You CAN subtract "shares" from "shares", of course, so I feel sure that what you intended was the second denominator to be "x- 15": the number of shares less the number NOT sold: the number of shares sold. Of course, then, the right hand side of the equation must also be in "dollars per share": $4/share would work nicely. Looks to me like the equation you intended to write was [tex]\frac{1895}{x} - \frac{1740}{x -15} = 4[/tex].
    Solve that for x.
     
  7. Mar 20, 2005 #6
    You're right, that was what I was going for. I had a typo in it earlier (x + 1 instead of x + 4), which was what made arildno react the way he did :p
     
  8. Mar 21, 2005 #7

    arildno

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    Yeah, I guess I overreacted a bit. Sorry..
     
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