What is the maximum product of two numbers that add to 24?

Let x and y represent the two numbers that add up to 24.

x + y = 24

=> y = 24 - x

The product of the two numbers is P = x*y = x*(24 - x) = 24x - x^2.

To maximize the product P, solve P' = 0 for x.

P' = 24 - 2x

24 - 2x = 0

=> x = 12

Also P'' = -2 which is negative

for x = 12

The product when x = 12 is 12*12 = 144

hope it helps!