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The drama club is selling tickets for a play. The profit, y, is modeled by the equation, y = x2 – 40x – 3,200, where x is the nu
Question
The drama club is selling tickets for a play. The profit, y, is
modeled by the equation, y = x2 – 40x – 3,200, where x is
the number of tickets sold. What is the total number of
tickets, x, that need to be sold for the drama club to break
even (profit = $0)?
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Mathematics
3 years
2021-08-31T08:02:05+00:00
2021-08-31T08:02:05+00:00 1 Answers
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Answers ( )
Answer:
80 tickets
Step-by-step explanation:
Given the profit, y, modeled by the equation, y = x^2 – 40x – 3,200, where x is the number of tickets sold, we are to find the total number of tickets, x, that need to be sold for the drama club to break even. To do that we will simply substitute y = 0 into the given the equation and calculate the value of x;
y = x^2 – 40x – 3,200,
0 = x^2 – 40x – 3,200,
x^2 – 40x – 3,200 = 0
x^2 – 80x + 40x – 3,200 = 0
x(x-80)+40(x-80) = 0
(x+40)(x-80) = 0
x = -40 and x = 80
x cannot be negative
Hence the total number of tickets, x, that need to be sold for the drama club to break even is 80 tickets