j_shreyans wrote:A certain movie star's salary for each film she makes consists of a fixed amount, along with a percentage of the gross revenue the film generates. In her last two roles, the star made $32 million on a film that grossed $100 million, and $24 million on a film that grossed $60 million. If the star wants to make at least $40 million on her next film, what is the minimum amount of gross revenue the film must generate?
A)$110 million
B)$120 million
C)$130 million
D)$140 million
E)$150 million
Let x= the film's gross revenue and y = star's salary.
The formula for determining the star's salary is the same as the EQUATION OF A LINE:
y = mx + b.
In the equation above:
m = the percentage of the film's gross revenue.
b = the fixed amount.
When we INPUT the value of x (the film's gross), the OUTPUT is the value of y (the star's salary).
The star made $32 million on a film that grossed $100 million.
Thus, when x=100, y=32, implying that one point on the line is (100, 32).
The star made $24 million on a film that grossed $60 million.
Thus, when x=60, y=24, implying that a second point on the line is (60, 24).
Since m = (y₂-y�)/(x₂-x�), we get:
m = (32-24)/(100-60) = 8/40 = 1/5.
The star wants to make at least $40 million on her next film.
Thus, when x is equal to a certain value, y=40, implying that a third point on the line is (x, 40).
Since (x, 40) and (60, 24) are both on the line -- and (y₂-y�)/(x₂-x�) = 1/5 for any two points on the line -- we get:
(40-24)/(x-60) = 1/5
16/(x-60) = 1/5
80 = x-60
x = 140.
The correct answer is
D.
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