Let's say the numbers are "a" and "b"
thus
![\bf y=ab\qquad \begin{cases} a+b=80\\ b=80-a \end{cases}\implies y=a(80-a)\implies y=80a-a^2\\\\ -----------------------------\\\\ \cfrac{dy}{da}=80-2a](https://tex.z-dn.net/?f=%5Cbf%20y%3Dab%5Cqquad%20%0A%5Cbegin%7Bcases%7D%0Aa%2Bb%3D80%5C%5C%0Ab%3D80-a%0A%5Cend%7Bcases%7D%5Cimplies%20y%3Da%2880-a%29%5Cimplies%20y%3D80a-a%5E2%5C%5C%5C%5C%0A-----------------------------%5C%5C%5C%5C%0A%5Ccfrac%7Bdy%7D%7Bda%7D%3D80-2a)
set the derivative to 0, and check the critical points, there's only one anyway
and do a first-derivative test, to see if it's a maximum
I think the answer is 3 < x < 8. Make sure to have the underlines underneath the < signs!
<span>number of people that attended the movie theater over the course of a month. hope that helped</span>