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

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A certain movie star's salary for each film she makes consis  [#permalink]

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New post 09 Aug 2010, 21:18
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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

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Re: Movie Salary  [#permalink]

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New post 10 Aug 2010, 02:04
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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
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Re: Movie Salary  [#permalink]

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New post 10 Aug 2010, 01:59
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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

can't really figure this out. any help would be great thanks!


Basically we have following linear relationship: Salary={Percent}*{Revenue from the film}+{Fixed amount} --> \(S=PR+F\) (the same as \(y=ax+b\)).

Given: \(32=100P+F\) and \(24=60P+F\). Question: if \(S\geq{40}\) then \(R_{min}=?\)

Solving: \(32=100P+F\) and \(24=60P+F\) --> subtract 2 from 1 --> \(8=40P\) --> \(P=0.2\) (so she gets 20% of the revenue) --> \(F=12\), so fixed amount is $12 million. So the formula for calculating star's salary is: \(S=0.2R+12\).

We want \(S=0.2R+12\geq{40}\) --> \(R\geq{140}\) --> so \(R_{min}=140\), if the star wants to make at least $40 million on her next film, the film must generate minimum $140 million of gross revenue.

Answer: D.

Hope it's clear.
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Re: Movie Salary  [#permalink]

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New post 10 Aug 2010, 11:55
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i figured it out as so:

a $60 million dollar gross = $24 million
and
a $100 million dollar gross = $32million

we can notice that the difference between the $100 million and $60 million is equal to $40 million. this $40 million equates to an $8 million salary ($32 - $24).

since we want $40 million in salary, we can add the $8 million difference to the $32 million. if we do that, we also need to add the $40 million difference ($100 - $60) to the $100 million. this gives us $140 million. our answer should be $140 million.

does this sound clear?
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Re: Movie Salary  [#permalink]

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New post 10 Aug 2010, 12:02
awesome explanation guys. thanks.
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Re: A certain movie star's salary for each film she makes consis  [#permalink]

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New post 25 Feb 2013, 11:34
Really awesome explanation.................
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Re: A certain movie star's salary for each film she makes consis  [#permalink]

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New post 10 Jan 2014, 06:43
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


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 :)
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A certain movie star's salary for each film she makes consis  [#permalink]

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New post 15 Feb 2015, 15:41
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.
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Re: A certain movie star's salary for each film she makes consis  [#permalink]

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New post 07 Mar 2018, 21:00
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

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Re: A certain movie star's salary for each film she makes consis  [#permalink]

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New post 04 Aug 2018, 08:06
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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 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
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