The sum of x and y is 100. How do you express the product P of the two numbers as a function of x?

Sep 7, 2016

$P = 100 x - {x}^{2}$

Explanation:

The two numbers add up to 100. We can define them both using just x, rather than having x AND y

If one of the numbers is $x$, the other number is $\left(100 - x\right)$.

Their product is P.
$P = x \times \left(100 - x\right)$

=$P = 100 x - {x}^{2}$