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algebra word problem

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find three consecutive positive numbers such that the product of the first and third minus the second, is 1 more than 6 times the third

  • algebra word problem -

    " find three consecutive positive numbers"
    Let the middle integer be M.

    "such that the product of the first and third minus the second,"
    (M-1)*(M+1) - M

    "is 1 more than 6 times the third"
    = 6(M+1)+1

    The resulting formula is therefore
    (M-1)(M+1)-M = 6(M+1)+1

    This equation has rational factors, or you could use the quadratic formula to find the solution. The answer for M is less than 10.

  • algebra word problem -

    I still don't understand it

  • algebra word problem -

    This is worked exactly the same way as mathmate did it but uses a little different terminology. Perhaps this will help.
    These are consecutive numbers; therefore, if we let x = first number, x + 1 = y is the second number and y+1 = z = the third number.
    Then product of 1st and 3rd is
    xz and that minus the second makes it
    xz-y and that = 6(3rd)+1 but the 3rd is 6z so
    xz-y=6z+1

    Now just substitute for x = y-1 and for z = y+1 and solve for y (which is the middle number).
    (y-1)(y-1) - y = 6(y+1)+1
    y=??
    y-1 = x
    y+1 = z

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