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Math Help - Another Quadratic Equation

  1. #1
    Junior Member
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    Another Quadratic Equation

    I buy a number of cheap calculators for a total of $240, mark each of them up by $2 and sell all but four of them for a total of $240. How many calculators did I buy?

    Okay, so this is what I have done so far:
    Let y represent the cost per calculator, and let x represent the number of calculator.
    Therefore, xy = 240
    And with the addition of the $2.00, minus the four pencils:
    (x-4)(y+2) = 240
    xy+2x-4y-8 = 240

    and now im stumped. what do i do?
    please explain + thanks in advance!

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  2. #2
    Member great_math's Avatar
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    Let x be the no. of calculators. Cost per calculator=$ \frac {240}{x}

    (x-4)\left(\frac {240}{x}+2\right)=240

    \Rightarrow (x-4)\left(\frac{240+2x}{x}\right)=240

    \Rightarrow (x-4)(240+2x)=240x

    \Rightarrow 240x+2x^2-960-8x=240x

    \Rightarrow 2x^2-8x-960=0

    \Rightarrow x^2-4x-480=0

    \Rightarrow (x+20)(x-24)=0

    \Rightarrow  x=-20(Impossible) or x=24

    So 24 is the required answer
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  3. #3
    Member great_math's Avatar
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    Quote Originally Posted by foreverbrokenpromises View Post
    I buy a number of cheap calculators for a total of $240, mark each of them up by $2 and sell all but four of them for a total of $240. How many calculators did I buy?

    Okay, so this is what I have done so far:
    Let y represent the cost per calculator, and let x represent the number of calculator.
    Therefore, xy = 240
    And with the addition of the $2.00, minus the four pencils:
    (x-4)(y+2) = 240
    xy+2x-4y-8 = 240

    and now im stumped. what do i do?
    please explain + thanks in advance!

    Now you have to substitute xy=240

    240+2x-4y-8=240

    \Rightarrow 2x-4y=8

    \Rightarrow  x-2y=4

    \Rightarrow x=4+2y

    Now xy=240

    \Rightarrow  (4+2y)y=240

    \Rightarrow 2y^2+4y-240=0

    \Rightarrow y^2+2y-120=0

    \Rightarrow (y+12)(y-10)=0

    \Rightarrow y=-12(not possible ) or y=10

    \Rightarrow x=4+2\times10=24
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