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Math Help - How to solve this problem algebraically?

  1. #1
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    How to solve this problem algebraically?

    Qs: One number is 6 more than another. Their product is 520. Find the numbers.

    -- Let the numbers be: x, x+6
    So, x(x+6) = 520
    or, x^2+6x=520
    then what..?

    The numbers are 20 & 26.
    And if I put them in the above formula, it works..
    20(20+6) = 520
    or, 20x26=520
    Last edited by peekayem; November 30th 2011 at 02:39 PM.
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  2. #2
    Super Member Quacky's Avatar
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    Re: How to solve this problem algebraically?

    x^2+6x-520=0

    Are you aware of any of the methods available for solving a quadratic equation?
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  3. #3
    Newbie mathland's Avatar
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    Re: How to solve this problem algebraically?

    One number is 6 more than another. Their product is 520. Find the numbers.

    Let any letter of choice be the number we are searching for. I will use n for number but you can use x, y, z, or whatever letter you like.


    Let n = one of the numbers

    Let n + 6 = the other number


    The words "Their product" should tell you right away that multiplication is what the question is leading to.

    n times (n + 6) = 250


    n(n + 6) = 250


    n^2 + 6n -250 = 0


    We have a quadratic equation.


    Use the quadratic formula.


    In the quadratic formula, let a = 1, b = 6 and c = -250.


    See link below to learn about this famous formula.

    The Quadratic Formula Explained

    If after visiting the site you have no clue what's going on, write back. I think it is important for you to try this one on your own. Keep in mind that x is typically used in the formula. Just replace my letter n with the typical variable x and follow the steps given in the link above.
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  4. #4
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    Re: How to solve this problem algebraically?

    Thanks for Both of the above posts. I've solved it using the factoring method e.g.
    factors of 520 that will match to x, x+6 are 20 & 26
    Since, x^2 + 6x -520 = 0
    (-20)(26) = -520
    (-20)+(26)= 6
    So, (x-20)(x+26)=0
    x-20 = 0, or x=20
    x+26 = 0, or x=-26
    x=20 ... this matches the equation, so the #s are 20 & 26.
    Will try the formula way also. Thanks again...
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