Profit, P, in dollars from the sale of x MP3 players is given with the following function.

P(x) = R(x) - C(x)

Where R(x) = x(350 - 0.000325 x^2)
and C(x) = 0.00015 x^3 + 100x
DETERMINE AN EQUATION FOR THE FUNCTION.

I.E if x = 100 then R = 34675 and C = 10150 so P = 24525

The back of the book gives me the answer as the equation being
P(x) = 250x - 0.000475 x^3.
Yes this works of course it works it gives me the same answer of 24525.
I just don't understand how the back of the book got that equation.

Is there anyone who can explain how that equation was created?

$\displaystyle P(x) = R(x) - C(x)$

$\displaystyle P(x) = x(350-0.000325x^2) - (0.00015x^3 + 100x)$

$\displaystyle P(x) = 350x-0.000325x^3 - 0.00015x^3 - 100x$

$\displaystyle P(x) = 250x - 0.000475x^3$