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$P = 47.4(G - 174.5)$ The profit, $P$ , in dollars, to an amusement park serving $G$ 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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Calculate unit rates with fractions

Full solution

Q.

P = 47.4(G - 174.5)

The profit,

P

, in dollars, to an amusement park serving

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?

Set Profit Greater Than Zero: To find the minimum number of guests needed to make a positive profit, we need to set the profit, $P$ , greater than zero and solve for $G$ . $P > 0$ $47.4(G - 174.5) > 0$
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 $G$ that makes the expression equal to zero and then determine the next whole number since we can't have a fraction of a guest. $47.4(G - 174.5) = 0$
Solve for G: Now we solve for G by dividing both sides of the equation by $47.4$ . $\newline$ $(G - 174.5) = 0 / 47.4$ $\newline$ $G - 174.5 = 0$
Isolate G: Next, we add $174.5$ to both sides of the equation to isolate $G$ . $\newline$ $G = 174.5$
Round Up to Next Whole Number: Since we can't have a fraction of a guest and we need more than $174.5$ guests to make a profit, we round up to the next whole number. $\newline$ $G = 175$

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