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Quadratic equations and inequalities / applications of quadratic functions question

  1. Nov 18, 2007 #1
    1. The problem statement, all variables and given/known data
    find two numbers whose sum is 20 and whose product is a maximum.

    2. Relevant equations
    the first number is X
    the second number is 20-x

    3. The solution
    -X^2+ 20x=0
    x=-b/2a = -20/2(-1) = 10
    20 - x =20 -10 = 10

    the numbers are 10 and 10

    i just dont get why / how you know to put x and 20 - x and why you would use the axis of symmetry to find the numbers

    and sry mods i posted originally in the wrong thread.
    Last edited: Nov 18, 2007
  2. jcsd
  3. Nov 19, 2007 #2


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    From the problem statement you have 2 numbers which sum to 20, that is x and 20-x.

    It should be obvious that ( x )+ (20 -x) = 20 so you have represented the 2 numbers in general. Now you need to find when the product x(20-x) is a maximum.

    Now if you were in a calculus class you would take the derivitive and set it to zero. Since you are not doing this I will have to assume that you are not in calculus. You have the problem of finding the maximum of the parabola, using properties of a parabola. The maximum will lie on the axis of symetry of the parabola, so all you need do is find the point on the parabola which lies on the symetry axis.
  4. Nov 19, 2007 #3
    not in calc but next year trig then pre and then calc
  5. Nov 19, 2007 #4


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    X(20-X)=0 is not true. You have the function 20X- X2 which is a parabola with maximum value at its vertex. You can find the (X,Y) coordinates of the vertex by completing the square.
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