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Math Help - quadratic equations

  1. #1
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    Question quadratic equations

    1)Rs,6500 were divided equally among a certain number of persons.if there had been 15 more person,each would have got Rs.30 less,find the original number of persons?
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  2. #2
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    Quote Originally Posted by anjana
    1)Rs,6500 were divided equally among a certain number of persons.if there had been 15 more person,each would have got Rs.30 less,find the original number of persons?
    write it out into an equation: \frac{6500}{p}=n

    now write out the second equation: \frac{6500}{p+15}=n-30\quad\Rightarrow\quad\frac{6500}{p+15}+30=n

    therefore: \frac{6500}{p}=\frac{6500}{p+15}+30

    Multiply both sides by "p+15" \frac{6500p+97500}{p}=6500+30p+450

    multiply both sides by p: 6500p+97500=6500p+30p^2+450p

    move everything to one side: -30p^2+6500p-6500p-450p+97500=0

    subtract: -30p^2-450p+97500=0

    and now you can use the quadratic formula (I hope you know how to do that)
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  3. #3
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    I might as well continue:

    using the quadratic formula you get: p=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

    substitute: p=\frac{-(-450)\pm\sqrt{(-450)^2-4(-30)(97500)}}{2(-30)}

    multiply: p=\frac{450\pm\sqrt{202500+11700000}}{-60}

    add: p=\frac{450\pm\sqrt{11902500}}{-60}

    find sqrt: p=\frac{450\pm3450}{-60}

    split equation: p=\left\{\begin{array}{cc}(450-3450)\div-60=-3000\div-60=50\\(450+3450)\div-60=3900\div-60=-65\end{array}\left

    therefore, after throwing away the negative answer, there were 50 people
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