vwjetty 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:
y = the movie's star salary
m = the movie's star's percentage of the gross revenue
x = the gross revenue
b = the fixed amount included in the movie star's salary
Since the movie star's salary consists of her percentage of the gross revenue plus the fixed amount, the result is the following equation:
y = mx + b
This is the EQUATION OF A LINE, where x = the gross revenue and y = the movie star's salary.
On a film that grossed $60 million, the star made $24 million.
On a film that grossed $100 million, the star made $32 million.In the other words, the following points are on the line above:
(60, 24)
(100, 32)
These two points indicates that the line has the following SLOPE:
The gross revenue increases by $40 million (here, from $60 million to $100 million) for every $8 million increase in the star's salary (here, from $24 million to $32 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?In accordance with the slope of the line:
For the star's salary to increase by another $8 million (from $32 million to $40 million), the gross revenue must increase by another $40 million (from $100 million to $140 million).
Thus, the gross required for a $40 million salary = $140 million.