A theatre company's profit can be modeled by the function P(x) = -60x^ + 700x -1000. Where x is the price of a ticket in dollars. What is the break-even price of the tickets?

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justaguide | College Teacher | (Level 2) Distinguished Educator

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In terms of the price of the ticket x, the profit of the theater company is modeled by the function P(x) = -60x^2 + 700x -1000. At break-even the company neither makes a profit nor a loss.

-60x^2 + 700x -1000 = 0

=> 6x^2 - 70x + 100 = 0

=> 6x^2 - 60x - 10x + 100 = 0

=> 6x(x - 10) - 10(x - 10) = 0

=> (6x - 10)(x - 10) = 0

=> x = 5/3 and x = 10

When the price of the ticket is $10 and when it is $1.66 the theater company breaks even.

oldnick's profile pic

oldnick | (Level 1) Valedictorian

Posted on

`f(x)=-60x^2+700x-100=10(-6x^2+70x-10)`

`6x^2-70x-10=0`

`Delta = 4900-240=4660>0`

`"2.real.solutions"`

`x=(70+-sqrt(4660))/12`

`x=(70+-2sqrt(1165))/6`

`x= (35+-sqrt(1165))/3`

`x_1=11,52 $`

`"Not.accetable.negative"`

`x_2=0,15 $`

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