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Answer:
she should charge $7.395 per ticket in order to make the most money.
Step-by-step explanation:
From the given information:
If Rosalie charges $5 then 1175 people will attend the circus performance
If Rosalie charges $7 then 935 people will attend the circus performance
Let x be the cost and y to be the number of people that will attend the performance . Then, we will have two points which are;
(5, 1175) and (7, 935)
The slope(m) of this points =
=
Slope (m) =
Slope (m) = -120
However; we can now have the linear equation:
The linear function is : y = -120x + 1775
Now; the total amount of money she can now earn is:
f(x) = xy
f(x) = x(-120x + 1775)
f(x) = -120x² + 1775x
The above expression is a quadratic equation; Using the quadratic formula; we have:
where; a = -120 ; b = +1775 and c = 0
= 0 OR 14.79
Since; we are considering the value greater than zero
x = 14.79
maximum value of x = 14.79/2 = 7.395
Thus ; she should charge $7.395 per ticket in order to make the most money.