Suppose 50 grams of dye is dissolved in a 500 liter tank. A solution of water and dye with a concentration 2 g/liter of salt is being pumped into the tank at a rate of 3 liters per minute. As the solution is being added, a well mixed solution in the tank is being drained out at the same rate.  Set up the initial-value problem where the solution to the differential equation will give the function for the amount of dye in the tank at time t, Q(t). The differential equation used in this mixing problem is

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