Problem Solving

alanforde800Maximus 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 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

alanforde800Maximus 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

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

32 - n = x

and

24 = x + n/100(60)

24 = x + 3n/5

Substituting, we have:

24 = 32 - n + 3n/5

-8 = -2n/5

-40 = -2n

20 = n

So x is 32 - 20 = 12.

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

Let's determine the gross revenue for a film that allows the movie star to earn 40 million.

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

28 = m/5

140 = m

Answer: D

Hi All,

This question involves what's called "system math", which is an algebra concept. We need to translate the given prompt into a couple of algebra equations, then solve.

We're told that a total is based on a fixed amount + a percentage of a gross. From the two roles, we can create the following equations:

X = fixed amount
Y = % of the gross

X + Y% of (100 million) = 32 million
X + Y% of (60 million) = 24 million

We now have a "system" of equations (2 variables with 2 equations, so we CAN solve for X and Y).

Subtracting the second equation from the first gives us...

Y% of (40 million) = 8 million
Y% = 8/40 = 1/5 = 20%
Y = 20

Plugging back into either equation, we get...

X+ 20% of (100 million) = 32 million
X = 12 million

With the value of X and Y, we can now answer the question: To make at least 40 million, the minimum gross revenue must be...

12 million + 20% of (Z) = 40 million
20% of (Z) = 28 million
Z = 140 million

Final Answer: D

GMAT assassins aren't born, they're made,
Rich