Let t = the first number
Let x = the second number

>>...the sum of the first and twice the second is 100...<<



We want to maximize the product xy.  

Let y = the product = tx



Solve  for t
      

Substitute  for t in









If you are taking algebra, not calculus, then find the
vertex of the parabola



Since the coefficient of  is negative, the
graph opens downward and thus reaches a maximum at the
vertex.

The formula for the x-coordinate of the vertex = 

So the x-coordinate of the vertex is 

So the value of x is 25

Now substitute 25 for x in 









So the two numbers are

first = 25
second = 50

---------------------------------------------

If you're taking calculus, you would do it by
taking the derivative of 





and set the derivative = 0







and as in the algebra way,  

Edwin