Textbook exercise I get stuck
"Amy is going to hold a concert at a stadium. The stadium can accommodate 12 000 people. If the price for each ticket is \$160, all the tickets will be sold. For every increase of \$1 in the ticket price, the number of tickets sold will decrease by 50. Let \$p be the price of each ticket and q be the number if tickets sold
(a) express $q$ in terms of $p$, where $p \geq 160$."
Please help!
The starting number of tickets sold is $12000\,\text{tickets}$. For each dollar above $160\,\$$, 50 fewer tickets are sold. The number of dollars above $160\,\$$ is \begin{equation} p-160\,\$\;. \end{equation} The number of tickets sold is therefore \begin{equation} q = 12000\,\text{tickets} - \left(50\,\frac{\text{tickets}}{\$}\right)(p - 160\,\$)\;. \end{equation}
Make sure you understand every part of the previous expression before moving on to part (b).
For part (b), you must use the total revenue from ticket sales: \begin{align} \text{Total revenue} &= \text{tickets sold}\times\text{price of tickets}\\ &=q\times p\\ &=\left(12000\,\text{tickets} - \left(50\,\frac{\text{tickets}}{\$}\right)(p - 160\,\$)\right)p\\ &\vdots \end{align} Now you can find the vertex or max point of the quadratic function.