When a school play charges $\$2$ for admission, an average of $100$ people attend. For each $10¢$ increase in admission price, the average number decreases by $1$. What charge would make the most money?
How do I convert this into a system of equations?
Note: For the question the system is supposed to be a parabola equation in vertex form, then find the maximum that way. For example:
A rancher is fencing off a rectangular area with a fixed perimeter of $76$m. What dimensions would yield the maximum area? Find the maximum area.
So then for this the equation would be $f(x)=3(x^2-8)+50$, solving by completing the square yields the answer of $19\times19; 361$.