$(8$ points$)$

A very large tank initially contains $100$ L of pure water. Starting at time $t=0$ a solution with a salt concentration of $0\mathrm{.}4k\frac{g}{L}$ is added at a rate of $5\frac{L}{m}in.$ The solution is kept thoroughly mixed and is drained from the tank at a rate of $3\frac{L}{m}in.$ Answer the following questions.

Let $y(t)$ be the amount of salt $($in kilograms$)$ in the tank after $t$ minutes. What differential equation does $y$ satisfy? Use the variable $y$ for $y(t).$ Answer $($in kilograms per minute$)$: $\frac{dy}{dt}=$

How much salt is in the tank after $50$ minutes?

Answer $($in kilograms$)$: