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Math Help - Quadratic help

  1. #1
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    Quadratic help

    A store owner buys a quantity of balls for $600. If they had each cost $0.25 less, she would have 10 more for the same money. How much did she pay for each ball.

    (x-0.25)*(y+10)
    is how far I got. Is this even a quadratic equation?
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  2. #2
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    Quote Originally Posted by sinjid9 View Post
    A store owner buys a quantity of balls for $600. If they had each cost $0.25 less, she would have 10 more for the same money. How much did she pay for each ball.

    (x-0.25)*(y+10)
    is how far I got. Is this even a quadratic equation?
    Hi sinjid9,

    the amount of money is the same in both cases and is (price)(quantity).

    Hence, if x=price, y=number of balls

    xy=(x-0.25)(y+10)=600

    Now write one variable in terms of the other using xy=600

    x=\frac{600}{y},\ or\ y=\frac{600}{x}

    This leads to the quadratic in a single variable.

    For example....

    (x-0.25)\left(\frac{600}{x}+10\right)=600

    \frac{1}{x}(x-0.25)(600+10x)=600

    (x-0.25)(600+10x)=600x

    600x+10x^2-150-2.5x=600x

    10x^2-2.5x-150=0

    100x^2-25x-1500=0

    4x^2-x-60=0

    (4x+15)(x-4)=0

    x-4=0 as x has to be positive.

    x=4\ dollars,\ y=150

    notice (4-0.25)(150+10)=(3.75)(160)=600
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