A school is holding a play. They have calculated that if they charge $\$10$ for the play, then $300$ people will attend the play. They have also calculated that for each $\$0.25$ decrease for the admission fee, $10$ more people will attend the play. How much should the school charge for admission to maximize profit?
My equation: $$(10-0.25x)(300+10x)=P$$ Expanding I get $$-2.5x^2+25x+3000=P$$ Using the formula $-\dfrac b{2a}$, I get that $x=\dfrac{-25}{-2.5}=10$. Then, plugging this back into the equation, I get that the school should charge $\$7.50$ for the play. My answer was incorrect; the correct answer is $\$8.75$. What did I do wrong?
yus another quadratic
Anyway, your $-\frac{b}{2a}$ is wrong this time; it should give $x=\frac{-25}{2(-2.5)}=5.$ So $F=8.75$ as a result, which is what we want.
(F is the fee)