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P=47.4(G174.5) P = 47.4(G - 174.5) The profit, P P , in dollars, to an amusement park serving G G guests over one day is given by the equation. What is the minimum number of guests that need to be served in order to make a positive profit?

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Q. P=47.4(G174.5) P = 47.4(G - 174.5) The profit, P P , in dollars, to an amusement park serving G G guests over one day is given by the equation. What is the minimum number of guests that need to be served in order to make a positive profit?
  1. Set Profit Greater Than Zero: To find the minimum number of guests needed to make a positive profit, we need to set the profit, PP, greater than zero and solve for GG.P > 047.4(G - 174.5) > 0
  2. Find Value of G: Since we want to find the minimum number of guests for a positive profit, we need to find the value of GG that makes the expression equal to zero and then determine the next whole number since we can't have a fraction of a guest.47.4(G174.5)=047.4(G - 174.5) = 0
  3. Solve for G: Now we solve for G by dividing both sides of the equation by 47.447.4. \newline(G174.5)=0/47.4(G - 174.5) = 0 / 47.4\newlineG174.5=0G - 174.5 = 0
  4. Isolate G: Next, we add 174.5174.5 to both sides of the equation to isolate GG. \newlineG=174.5G = 174.5
  5. Round Up to Next Whole Number: Since we can't have a fraction of a guest and we need more than 174.5174.5 guests to make a profit, we round up to the next whole number.\newlineG=175G = 175

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