Let X(t) be the pounds of concetrate in the tank at time t minutes. Since there are 5 gallons of water coming into the tank per minute and 3 gallons going out each minute, their are a net 5- 3= 2 gallons coming in each minute and the volume of water in the tank is 100+ 2t at time t minutes (so it will be full when 100+2t= 200, 2t= 100, t= 50 min as given). The concentration at time t min. is X(t)/(100+ 2t).
dX/dt is the net rate at which concetrate is going into the tank. We know that the 5 gallons of water coming into the tank each minute carries in 0.5 pounds per gallon. How many pounds is that per minute coming in?
Water goes out at 3 gallons per minute and carries X(t)/(100+2t) pounds with it. How many pounds is that per minute?
What is the net rate at which the concentrate is coming in per minute? Can you set up the differential equation from that?