Inactive Tutor answered • 04/14/16
Tutor
New to Wyzant
0=x^2-190x+7425
=(x-135)(x-55)
Laura H.
asked • 04/10/16Algerbra/Statistics Word Problem
A 5000 seat theatre has tickets for sale at $25 and $40. How many tickets should be sold at each price for a sellout performace to generate a total revenue of $141,500?
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2 Answers By Expert Tutors
Inactive Tutor answered • 04/10/16
Tutor
New to Wyzant
You can solve this using a system of equations.
x=number of seats for sale for $25
y= number of seats for sale for $40
You want x+y=5000
And you want the total revenue to be $141,500 so 25x+40y=141,500.
You can solve for x in the first equation to plug into the second equation.
x=5000-y
25(5000-y)+40y=141,500
Solve for y using algebra. (If you need help with this step, let me know.)
Then plug y back in the first equation and solve for x.
Good luck!!
Inactive Tutor
Is the R(x) the revenue equation and C(x) costs?
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04/10/16
Laura H.
Yes. Trying to find the break even point. And I am at a loss...
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04/10/16
Laura H.
Any luck?
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04/10/16
Inactive Tutor
For a break even point, you want the costs to be equal to the revenues (0 profit). So you should set the two equations equal to each other.
200x - 2x2 = -x2 + 10x +7425
Combine like terms.
190x - x2 = 7425
Then you've essentially got a quadratic equation that could be solved with factoring or by graphing it. I would use a graphing calculator to try to plot it (-x2 + 190x -7425=y) and see where the x-intercepts are. You could also just plug the two equations into a graphing calculator to see where they intersect.
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04/10/16
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Laura H.
04/10/16