Algebra

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Don't understand quadratic word problems at all. Please help, with steps.

One number is 8 more than another number. Their product is 273. find the numbers.

The differance between a number and twice it's reciprocal is 17/10. What is the number?
Thanks,
Kelly

  • Algebra -

    y = x + 8
    x*y = 273

    x*(x+8) = 273
    x^2 + 8x - 273 = 0

    (x-13)(x+21) = 0

    One of those factors must evaluate to 0 for the answer to be 0. Therefore, x must equal either 13 or -21.

    y must equal either 21 or -13.

    So: x=13 and y=21
    or x=-21 and y=-13

    I'm sure you can figure out the second one.

  • Algebra -

    For the first problem:
    Let x = lesser number
    let y = greater number
    (x) (y) = 273
    The problem states that y = x + 8.
    substituting for y:
    (x) (x+8)=273
    x^2 + 8x=273
    so
    x^2 + 8x - 273 = 0
    Solve for x.
    Then, y = x + 8

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