## A certain movie star's salary for each film she makes consists of a fixed amount, along with a percentage of the gross

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### A certain movie star's salary for each film she makes consists of a fixed amount, along with a percentage of the gross

by Gmat_mission » Sun Sep 19, 2021 1:11 pm

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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

Source: Manhattan GMAT

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### Re: A certain movie star's salary for each film she makes consists of a fixed amount, along with a percentage of the gro

by [email protected] » Sun Sep 19, 2021 2:15 pm
Gmat_mission wrote:
Sun Sep 19, 2021 1:11 pm
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

Source: Manhattan GMAT
Let F = the fixed amount the star receives for a movie
Let p = the percentage of the gross revenue the star receives for a movie

The star made $32 million on a film that grossed$100 million
So, we can write: F + (p/100)(100) = 32 [we'll assume that 100 and 32 represent 100 million and 32 million]

The star made $24 million on a film that grossed$60 million
So, we can write: F + (p/100)(60) = 24

We now have:
F + (p/100)(100) = 32
F + (p/100)(60) = 24

Subtract the bottom equation from the top equation to get: (p/100)(100) - (p/100)(60) = 8
Factor to get: (p/100)[100 - 60] = 8
Simplify to get: (p/100) = 8
Multiply both sides by 100 to get: 40p = 800
Solve: p = 20

Now that we know the value of p, we can find the value of F
Take F + (p/100)(100) = 32 and replace p with 20 to get: F + (20/100)(100) = 32
Simplify: F + 20 = 32
So, F = 12

So, the star receives 12 million (fixed) PLUS 20% of the gross revenue

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?
Let x = gross revenue the film must generate
We can write: 12 + 20% of x = 40
Rewrite as: 12 + 0.2x = 40
Subtract 12 from both sides: 0.2x = 28
Solve: x = 140 (million)