AAPL wrote:Manhattan Prep

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

OA D

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)[40] = 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)

Answer: D

Cheers,
Brent

AAPL wrote:Manhattan Prep

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

OA D

We can let x = the fixed amount, in millions, the movie star receives and n/100 = the percentage of the gross revenue from the film that she receives. Therefore, we can create the equations:

32 = x + n/100(100)

32 = x + n → Eq. 1


and

24 = x + n/100(60)

24 = x + 3n/5 → Eq. 2

Subtracting Eq. 2 from Eq. 1, we have:

8 = 2n/5


40 = 2n

20 = n

Using Eq. 1, we see that x = 32 - 20 = 12.

Thus, we see that she earns a fixed amount of $12 million per film and 20% of the film's gross revenue.

Let's determine the gross revenue m for a film that allows her to earn $40 million.

40 = 12 + (1/5)(m)

28 = m/5

140 = m

Answer: D