Maths-
General
Easy
Question
A theatre company uses the revenue function
dollars. The cost functions of the production
. What ticket price is needed for the theatre to break even?
Hint:
The expansion of the expression is
.
We are asked to find the ticket price that is required to break it even for revenue and cost production function.
The correct answer is: We are asked to find the ticket price that is required to break it even for revenue and cost production function.
Step 1 of 3 :
The revenue function of the theatre company is
.
The cost functions production is
.
To break it even, the cost function and the revenue function must be the same.
That is, they should at least have the same value.
That happens when they are equal, so:
![450 minus 50 x equals negative 50 x squared minus 250 x](data:image/png;base64,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)
Step 2 of 3:
Rearrange and simplify the equation,
![table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell 450 minus 50 x equals negative 50 x squared plus 250 x space space end cell row cell 50 x squared minus 250 x plus 50 x plus 450 equals 0 end cell row cell 50 x squared minus 300 x plus 450 equals 0 space space space space space space space space space space space end cell row cell x squared minus 6 x plus 9 equals 0 space space space space space space space space space space space space space space space space space space space space space space space end cell end table](data:image/png;base64,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)
Here, we took out 50 from the equation to simplify it.
Step 3 of 3:
Solve the simplified equation.
![table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell x squared minus 6 x plus 9 equals 0 space space space space space space space space space space space space end cell row cell x squared minus 3 x minus 3 x plus 9 equals 0 space space space space end cell row cell x left parenthesis x minus 3 right parenthesis minus 3 left parenthesis x minus 3 right parenthesis equals 0 end cell row cell left parenthesis x minus 3 right parenthesis squared equals 0 space space space space space space space space space space space space space space space space space space end cell row cell x equals 3 space space space space space space space space space space space space space space space space space space space space space space space space space space space space end cell end table](data:image/png;base64,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)
Thus, they should sell the ticket at least at three dollars to even it out.
The maximum number of solutions possible for a quadratic equation is two. It cannot have solutions more two.
Related Questions to study
Maths-
Rewrite the equation as a system of equations, and then use a graph to solve.
![0.5 x squared plus 4 x equals negative 12 minus 1.5 x](data:image/png;base64,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)
Rewrite the equation as a system of equations, and then use a graph to solve.
![0.5 x squared plus 4 x equals negative 12 minus 1.5 x](data:image/png;base64,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)
Maths-General
Maths-
Rewrite the equation as a system of equations, and then use a graph to solve.
![x squared minus 6 x equals 2 x minus 16](data:image/png;base64,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)
Rewrite the equation as a system of equations, and then use a graph to solve.
![x squared minus 6 x equals 2 x minus 16](data:image/png;base64,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)
Maths-General
Maths-
Find the simple interest on Rs. 6500 at 14% per annum for 73 days?
Find the simple interest on Rs. 6500 at 14% per annum for 73 days?
Maths-General
Maths-
Rewrite the equation as a system of equations, and then use a graph to solve.
![2 x squared plus 3 x equals 2 x plus 1](data:image/png;base64,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)
Rewrite the equation as a system of equations, and then use a graph to solve.
![2 x squared plus 3 x equals 2 x plus 1](data:image/png;base64,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)
Maths-General
Maths-
Rewrite the equation as a system of equations, and then use a graph to solve.
![4 x squared equals 2 x minus 5](data:image/png;base64,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)
Rewrite the equation as a system of equations, and then use a graph to solve.
![4 x squared equals 2 x minus 5](data:image/png;base64,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)
Maths-General
Maths-
Find the simple interest on Rs. 8000 at 16 % per annum for 9 months?
Find the simple interest on Rs. 8000 at 16 % per annum for 9 months?
Maths-General
Maths-
The simple interest on a sum of money at the end of 5 years is of the sum. Find the rate of interest?
The simple interest on a sum of money at the end of 5 years is of the sum. Find the rate of interest?
Maths-General
Maths-
Find the solution of the system of equations.
![y equals 2 x squared plus 5 x minus 30](data:image/png;base64,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)
y = 2x + 5
Find the solution of the system of equations.
![y equals 2 x squared plus 5 x minus 30](data:image/png;base64,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)
y = 2x + 5
Maths-General
General
Format the sentence into converts Spanish grammar.
"My wife buys a new television for my father”
Format the sentence into converts Spanish grammar.
"My wife buys a new television for my father”
GeneralGeneral
General
Find the helping Verbs and Action Verbs in the following sentences.
Find the helping Verbs and Action Verbs in the following sentences.
GeneralGeneral
Maths-
If Rs. 4000 amounts to Rs. 4500 in 2 years, find how much would it amount in 5 years at the same rate of interest?
If Rs. 4000 amounts to Rs. 4500 in 2 years, find how much would it amount in 5 years at the same rate of interest?
Maths-General
Maths-
Find the solution of the system of equations.
![y equals 3 x squared plus 2 x plus 1](data:image/png;base64,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)
![y equals 2 x plus 1](data:image/png;base64,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)
Find the solution of the system of equations.
![y equals 3 x squared plus 2 x plus 1](data:image/png;base64,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)
![y equals 2 x plus 1](data:image/png;base64,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)
Maths-General
Maths-
Find the solution of the system of equations.
![y equals x squared plus 8 x plus 30](data:image/png;base64,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)
y = 5 - 2x
Find the solution of the system of equations.
![y equals x squared plus 8 x plus 30](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHgAAAATCAYAAABbV8lLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAArNJREFUeNrtWVFkW1EYvq6ImBgTUbOHEVUzE2NPNVVhKqaqQsweaqYvtYe571V9qFFVMTOjpmamStUeKmLMTMzUmJmqqjB72EPlpQ81EVHS/+dLnZ6dG0nOPbnLdT8+7jn3JPfP+f/z/f9/Y1n/L5pgg/iVOGyFCCRs4hPij3Argo16uAXBxTixHG5DMHEVOThl6PsvEV8Q/0IlPhCv+fybM8QSsQabKsTnxIRi7WXiK+I3cA1zA4ERYhFONoV14jNihBglLmOj/MRnYg72tHAbwSfjE3FKGE9ibiBObqnHaGxq5HYblbupzkAHJ9I4D/WRwaf9oRzFDxQLHUS3l5jFKZGxhHstsHNv9GEjWZrjkoP/aNhtysGcog6luW3ihIvEb4sTj4gritxUcdH9ZgdsB255hoTxY+LLDp5hwsF8Ap4K41HiqobdXjt4CM9hX9yX7h1LMt4Cz1XFCf7glrRokbhgSKqyxAKu7xnIGd1sZBqS3EClfkQcM2R3t0Eq0lGsOW3z+Qtphk/pvjBOEn8RYwZz7Ee0Pz9dVMLS2IxOT/914gbyfesk3MFvT3tgt67SMa4Qp1H4jXfh4H/eG9SE64JLxHhpuIMoS/tYzLx3eX4GlazXduvk4Liiuq+6SHRMlmjGFyTyFCLYNnh676IIKMjVXp8dXO/ynq7dulV0XVFkZRXrJuQii/EW/RRL1oxB53IA7aCI46j87oFE97qRB5b6T4ybyMVe263j4DQKLRHcK79WrH2jCkAH7dKeQecm0f4kpMb8nU8OzsHJGSiWjWtWsDkDdndqVxk9bkSw6Te6HdVLEUd4UTNvubzWnYYBU4acG0XOU70G3HSRmn4gj/anAQksYy/8tJur+CLsqcOJk22KsHWs4zpqTerrz8GO3bVCBBYlNPkhAohbkIQQAcMZmiPI9pZHhi0AAACndEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1pPnk8L21pPjxtbz49PC9tbz48bXN1cD48bWk+eDwvbWk+PG1uPjI8L21uPjwvbXN1cD48bW8+KzwvbW8+PG1uPjg8L21uPjxtaT54PC9taT48bW8+KzwvbW8+PG1uPjMwPC9tbj48L21hdGg+ZI0xqgAAAABJRU5ErkJggg==)
y = 5 - 2x
Maths-General
Maths-
At what rate percent per annum will a sum of money double itself in 10 years?
At what rate percent per annum will a sum of money double itself in 10 years?
Maths-General
Maths-
Find the solution of the system of equations.
![y equals x squared plus 6 x plus 9](data:image/png;base64,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)
y = 3x
It is not necessary for every set of equation to have solutions. If you graph them and get not intersecting points, then they have no real solutions.
Find the solution of the system of equations.
![y equals x squared plus 6 x plus 9](data:image/png;base64,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)
y = 3x
Maths-General
It is not necessary for every set of equation to have solutions. If you graph them and get not intersecting points, then they have no real solutions.