Let's compute the time it takes for the tank to have 100 gallons of fluid. We will denote this time by $t$. Initially, there are $75$ gallons of fluid. We add brine at a rate of $4$ gal/min and remove it at a rate of $3$ gal/min, so the net increase in fluid each minute is $4-3=1$ gallon/min. Therefore, it takes $t$ minutes to increase the amount of fluid in the tank from $75$ gallons to $100$ gallons, so we solve $75+t=100$ to find $t=25$ minutes.
During these $25$ minutes, we pump brine at a rate of $4$ gal/min, so the total amount of salt we pump into the tank is $0.5\text{ pounds/gal}\times 4\text{ gal/min}\times 25 \text{ min}=50$ pounds.
Note that since the amount of fluid in the tank changed, the concentration of salt in the tank is higher than it was initially. Initially, we had $2$ pounds of salt dissolved in $75$ gallons of fluid, so the initial concentration was $2/75$ pounds/gallon. After pumping brine for $25$ minutes, we have a total amount of $75+4\times 25=175$ gallons of fluid, so the concentration is now the ratio of the total amount of salt to the total amount of fluid, or $50/175=0.285714$ pounds/gallon.
Therefore, when there are $100$ gallons of fluid in the tank, there will be approximately $\boxed{28.57}$ pounds of salt in the tank.
A large tank contains 75 gallons of brine in which 2lb of salt is dissolved. Suppose we pump brine at a concentration of 0.5 pounds per gallon into the tank at a rate of 4 gallons per minute. We then pump the mixture out of the tank at a rate of 3 gallons per minute. How much salt will be in the tank at the moment that there are 100 gallons of fluid in the tank? Round your answer to decimal places.
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