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Nguyen has opened a new bake shop in town selling pies. Nguyen sells each pie for $\mathrm{}9$$9 and has spent $\mathrm{}1,311$$1,311 on rent and maintenance this month. How many pies did Nguyen sell if he made $\mathrm{}399$$399 profit this month? See Answers Get the Answer.AI App Solve problem with AI Best Answer Let $x$x be the number of pies Nguyen sold. The revenue from selling $x$x pies is the product of the price per pie and the number of pies: Revenue $=9x$=9x The cost of selling $x$x pies is the sum of the fixed costs (rent and maintenance) and the cost per pie (which we don’t know): Cost $=1,311+cx$=1,311+cx where $c$c is the cost per pie. The profit for selling $x$x pies is: Profit $=9x-\left(1,311+cx\right)$=9x-(1,311+cx) We know that Nguyen made a profit of $\mathrm{}399$$399, so we can set up the equation:
$9x-\left(1,311+cx\right)=399$9x-(1,311+cx)=399
Solving for $c$c using the information given in the problem:
$399=9x-\left(1,311+cx\right)$399=9x-(1,311+cx)
$399=9x-1,311-cx$399=9x-1,311-cx
$cx=9x-1,710$cx=9x-1,710
$c=\frac{9x-1,710}{x}$c=(9x-1,710)/(x)
Plugging this expression for $c$c back into the equation:
$9x-\left(1,311+\frac{9x-1,710}{x}\right)=399$9x-(1,311+(9x-1,710)/(x))=399
Multiplying both sides by $x$x to eliminate the fraction:
$9{x}^{2}-1,311x+9x-1,710=399x$9x^(2)-1,311 x+9x-1,710=399 x
Simplifying:
$9{x}^{2}-703x-1,710=0$9x^(2)-703 x-1,710=0
We can solve for $x$x using the quadratic formula:
$x=\frac{-\left(-703\right)±\sqrt{\left(-703{\right)}^{2}-4\left(9\right)\left(-1710\right)}}{2\left(9\right)}$x=(-(-703)+-sqrt((-703)^(2)-4(9)(-1710)))/(2(9))
Simplifying:
$x=\frac{703±\sqrt{497,209+61,560}}{18}$x=(703+-sqrt(497,209+61,560))/(18)
$x=\frac{703±\sqrt{558,769}}{18}$x=(703+-sqrt(558,769))/(18)
$x=\frac{703±747}{18}$x=(703+-747)/(18)
The positive root gives the number of pies that Nguyen sold:
$x=\frac{703+747}{18}=\frac{1450}{18}\approx 80.56$x=(703+747)/(18)=(1450)/(18)~~80.56
Rounding down since Nguyen can’t sell a fraction of a pie, he sold $\overline{)80}$80 pies.
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