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

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 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

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.

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

Re: A certain movie star's salary for each film she makes consis [#permalink]
07 Feb 2015, 09:33

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A certain movie star's salary for each film she makes consis [#permalink]
15 Feb 2015, 14:41

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.

gmatclubot

A certain movie star's salary for each film she makes consis
[#permalink]
15 Feb 2015, 14:41

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