la sallle

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There are 3 consecutive even integers such that the quotient obtained by dividing twice the largest integer by the smallest integer is three less than three-fifths of the second integer. What are the integers?

  • la sallle -

    Three consecutive even integers are:
    2n, 2n+2, 2n+4, where n is an integer.

    The rule is thus:
    2(2n+4)/2n = (3/5)(2n+2) - 3

    Rearranging gives:
    0 = 6 n2 - 19n - 20

    Find the integer root(s) of this quadratic. Solve for integer n.

    Use n to find the three consecutive even numbers.

  • la sallle -

    I would let my 3 consecutive even integers be
    x-2, x, and x+2

    2(x+2)/(x-2) =3x/5 - 3
    expanding and collecting like terms gives us
    3x^2 - 31x + 10 = 0
    (x-10)(3x - 1) = 0
    x = 10 or x = 1/3, but x is an integer, so

    x = 10

    the integers are 8, 10 , and 12

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