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Quadratic equations and inequalities / applications of quadratic functions question

  • Thread starter ben328i
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  • #1
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Homework Statement


find two numbers whose sum is 20 and whose product is a maximum.


Homework Equations


the first number is X
the second number is 20-x



3. The solution
X(20-X)=0
-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:

Answers and Replies

  • #2
Integral
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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.
 
  • #3
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thanks
not in calc but next year trig then pre and then calc
 
  • #4
HallsofIvy
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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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