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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] New post 09 Aug 2010, 20:18
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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
[Reveal] Spoiler: OA

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Re: Movie Salary [#permalink] New post 10 Aug 2010, 00:59
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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] New post 10 Aug 2010, 01:04
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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] New post 10 Aug 2010, 10:55
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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] New post 10 Aug 2010, 11:02
awesome explanation guys. thanks.
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Re: A certain movie star's salary for each film she makes consis [#permalink] New post 25 Feb 2013, 10:34
Really awesome explanation.................
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Re: A certain movie star's salary for each film she makes consis [#permalink] New post 10 Jan 2014, 05:43
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 :)
Re: A certain movie star's salary for each film she makes consis   [#permalink] 10 Jan 2014, 05:43
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