A certain movie star's salary for each film she makes consis

answer is D.
Let x be fixed income
Let y be the % of variable income.
x+(y/100)*100 = 32
x+(y/100)*60 = 24
so we get x = 12 and y = 20%
then
x+0.2(required revenue)= 40. we get required revenue = 140 million dollars

Movie star earned 8 million more in salary with an increase in 40 movie. That is a ratio of 5 times
Therefore in order to gain 40 mil she needs an increase of 8 million, which will correspond to an increase in (8*5 = 40 million) in movie

Thus 140 is your best choice

Hope it helps
Cheers
J

awesome explanation guys. thanks.

Really awesome explanation.................

I used sort of a longer approach and it took me almost 4 minutes to solve... But, for those that can calculate fast and don't have to correct calculation mistakes I guess it wouldn't be a problem:

Z is the fixed amount, x/100 the percentage of the revenue she gets and R the revenue of the film. So:
\(Z+\)\(\frac{x}{100}\) \(* 100 = 32\), and

\(Z+\)\(\frac{x}{100}\) \(* 60 = 24\)


We subtract the second equation from the first one which leads to:
\(\frac{2x}{5}\) \(= 8\)

\(2x = 40\)

\(x = 20\). So we have the % she earns from the revenue of the film.

We replaxe x for 20 in one of our equations:
\(Z+\)\(\frac{x}{100}\) \(* 100 = 32\)

\(Z+\)\(\frac{20}{100}\) \(* 100 = 32\)

\(Z = 12\), So, we have the fixed amount.

Now, we know that she wants to get 40 on the next film. So,
\(12 +\) \(\frac{20}{100}\)\(*R = 40\)

\(12+0.2R = 40\)

\(0.2R = 28\)

\(R = 140\).

So, ANS 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:

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

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

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

putting equations with 100 as denominator will be time consuming. the best way is

F + 100y = 32
F + 60y = 24

Subtract both you get: 40y = 8 therefore y = 1/5

original equation:
F + 20 = 32
hence, F = 12
atleast 40 needed, so 40 - Fixed = 28

D 140 * 1/5 = 28

Done!

We can see that,
The movie star makes $32 million on $100 million gross revenue
And,
$24 million on $60 million gross revenue

We see,
If gross revenue decreases $40 million, the amount movie star makes decreases by $8 million

So, if the amount movie star makes, increases by $8 million(40 - 32) ,
Then,
gross revenue increases by $40 million

So, Total gross revenue= $100 + $40 = $140
OA (D)

How do we know that she makes a constant % from gross revenues.?

We know she gets a fixed pay and the variable pay. But is it right to assume that the variable pay % per movie is the same?

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.

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