SOLUTION: Find two numbers whose sum is
28 and whose product is the maximum possible value.
What two numbers yield this product?
Algebra.Com
Question 1138954: Find two numbers whose sum is
28 and whose product is the maximum possible value.
What two numbers yield this product?
Found 2 solutions by josmiceli, rothauserc:
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let one of the number be
and
Both numbers are 14
check:
Here's the plot:
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
let x, y be the two numbers
:
x + y = 28
:
if the two numbers are 1 and 27, then
:
1) x + y = 28
:
2) xy = 27
:
solve equation 1 for y, then substitute for y in equation 2
:
3) y = 28 -x
:
x(28-x) = 27
:
4) -x^2 +28x -27 = 0
:
the graph of equation 4 is a parabola that curves downward, so the coordinates of the vertex is the maximum values for x and y
:
x coordinate = -b/2a = -28/2(-1) = 14
:
substitute for x in equation 3
:
y = 28 -14 = 14
:
*****************************************************
the maximum product occurs when x=14 and y=14
:
Note 14 * 14 = 196
*****************************************************
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