At time $t=0$, a tank contains 30 oz of salt dissolved in 100 gallons of water. Then brine containing 8oz of salt per gallon of brine is allowed to enter the tank at a rate of 2 gal/min and the mixed solution is drained from the tank at the same rate.

How much salt is in the tank at an arbitrary time?

So the way I write the differential is $\frac{dS}{dt}=S_{in}-S_{out}$, where $S_{in}$ is the rate of salt going in and $S_{out}$ is the rate of salt coming out. The differential I obtained is $\frac{dS}{dt}=16-\frac{3}{50}S$ and the solution to be $S=\frac{800}{3}-\frac{7991}{3}e^{\frac{-3t}{50}}$. I'm unsure of what went wrong but the webwork keeps rejecting my answers.


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