What the heck does this question mean?

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DIFFERENTIATION QUESTION. EXAM TOMMORROW. PLEASE HELP ME! A QUESTION LIKE THIS IS GUARANTEED TO COME UP. AND I HATE THESE TYPES, NOT DIFFERENTIATION IN GENERAL THOUGH.

P=xy and 2x+5y=100
a). Express P as a fuction of x.
b). Find the maximum value of P
c). State the values of x and y that give the maximum value of P

The bold part indicates the part that I have no clue about to get.

The answers are
a). 20x - 2/5x^2
b). 250
c). x=25, and y=10

How the HELL did they get the answer to a) as 20x - 2/5x^2

so p=xy and 2x + 5y = 100

so y = p/x

so 100 = 2x + 5p/x

so 5p/x = 100 - 2x

so 5p = x(100 - 2x)

so 5p = 100x - 2x^2

so p = 100x/5 - 2/5x^2

so p = 20x - 2/5x^2

So when it says expree as a for of x... you really want the f(x) of p?

It means you want to get rid of the y.

"P=xy and 2x+5y=100"

So...

5y = 100 - 2x
y = 20 - 2/5x

Then

P = x(20 - 2/5x)