SOLUTION: What is the maximum product of two numbers that add to 18? What numbers yield this product?

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: What is the maximum product of two numbers that add to 18? What numbers yield this product?      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 724086: What is the maximum product of two numbers that add to 18? What numbers yield this product?
Answer by josgarithmetic(39629) About Me  (Show Source):
You can put this solution on YOUR website!
Two numbers, p=xy, and x+y=18, so y=18-x. Substitute to see p=x(18-x), p=18x-x^2,
highlight%28p=-x%5E2%2B18x%29.

p is a function of x and it has a maximum. How to solve the rest depends on choosing basic Algebra or choosing Calculus using a derivative.

Completing the Square:
(Because when multiply by -1, sign changes).
=-1%28x-9%29%5E2%2B81

highlight%28p=-1%28x-9%29%5E2%2B81%29

ANSWER: The MAXIMUM will be at x=9, where p=81
Note: Some of this solution is NOT being rendered correctly in the system but I DID write it correctly.