MGMAT Q' s Equation formation-algebra

Question

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? 
 $110 million 
 $120 million 
 $130 million 
 $140 million 
 $150 million 
 
 $140 million

bangalorian2000 · Answer

Let x be fixed amount & y is the %age
1st eqn: x+y/100(60) = 24
2nd eqn: x+y/100(100) = 32
solving we get x=12, y=20

for $40million profit, 12+1/5(z) = 40
z=140

nverma · Answer

Let c be the constant amount, G be the gross revenue and v be the variable as a percentage of the gross revenue. 
So from first condition.

c + (V/100)*G = 32
c + (V/100)*100 = 32 ..........................(1)

and from the second equation..

c + (V/100)*G = 24
c + (V/100)*60 = 24 ..........................(2)

From equations 1 and 2, we can find c and v, so c = 12 and v = 20.

So to have total income of 40.

12+ (20/100)*G =40... the movie should gross, G= 140.

sidhu4u · Answer

Let's say fixed amount is x and r is the percentage of gross amount

so from first movie 32 = x+100r/100=>32=x+r
from second movie 24 = x+r60/100 => 24 = x+3r/5 => 24 = 32-r+3r/5 => 2r/5 = 8 => r = 20 and x = 12

to get 40 million from the next movie
40 = x+r*g/100 => 40 = 12+20/100 *g => g = 28*100/20 => g = 140

So next movie should generate140 million

mustdoit · Answer

Let fixed cost = x and variable =y

we have 
x+100y = 32
x+ 60y= 24

solving we get y = 1/5 and x = 12

so to earn 40 in her next film he needs

12+ .2y=40
y= 140 answer.

Hope this helps !!!

dimitri92 · Answer

I would tackle it in a less conventional way ....

the two equations are indeed

c + (V/100)*100 = 32 ..........................(1)

c + (V/100)*60 = 24 ..........................(2)

now note that this is pretty much same as a graph of y = mx +c

this means that the slope will always be the same ....i.e m

lets see what the slope is based on the two eqns = 32 - 24 / 100 - 60 = 8 / 40

so for every increment of 8 in the salary we have a 40 increase in the Revenue

this is the same as the jump from 32 to 40 which is a jump of 8 so it will require a Revenue jump of 40 ...thus from 100 to 140 ...which is the answer

KarishmaB · Answer

This can be easily tackled by considering the variable part only since fixed part is the same in each case: 
$32 mil from $100 mil
$24 mil from $60 mil
So she earned an extra 8 mil when the film made 40 mil extra. 
Now, if she wants to get $40 mil from her next movie i.e. 8 mil more than $32 mil, the movie should gross 40 mil more than $100 mil i.e. a total of $140 mil.

anon321 · Answer

This can also be solved using the Linear Interpolation formula:

y= y_a + (y_b - y_a)\frac{(x - x_a)}{(x_b - x_a) }  at the point (x,y)

So that becomes:

40=24 + (32-24)\frac{(x-60)}{(100-60)}

Solving this equation for  x  should be pretty straight-forward.

You get  x=140

144144 · Answer

wow Karishma. thanks.

MGMAT Q' s Equation formation-algebra

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