SOLUTION: Among all pairs of numbers whose sum is negative eighteen (-18), find the pair of numbers whose product is as large as possible. Evaluate algebraic methods for solving the problems

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: Among all pairs of numbers whose sum is negative eighteen (-18), find the pair of numbers whose product is as large as possible. Evaluate algebraic methods for solving the problems      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 808467: Among all pairs of numbers whose sum is negative eighteen (-18), find the pair of numbers whose product is as large as possible. Evaluate algebraic methods for solving the problems and show your work. What are the numbers? What is the maximum product?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Among all pairs of numbers whose sum is negative eighteen (-18), find the pair of numbers whose product is as large as possible. Evaluate algebraic methods for solving the problems and show your work. What are the numbers? What is the maximum product?
----------
Equations:
x + y = -18
-----
Product:: P(x) = xy = x(-18-x)
-----
P(x) = -x^2-18x
------
Maximum profit occurs when x = -b/(2a) = 18/(2*-1) = -9
====
Solve for "y":
x + y = -18
-9 + y = -18
y = -9
=====
Answer: The numbers are -9 and -9.
The maximum product is -9*-9 = 81
======================
Cheers,
Stan H.
======================
=================
-----