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? Answer in terms of $ millions.

Answer 1

$140 MN

Step-by-step explanation:

Salary = %age of Gross Revenue + Fixed amount

For A:

32 = x% of 100 + y

For B:

24 = x% of 60 + y

Subtracting A and B

8 = x% of 40

x = 20%

Solve for y:

24 = 20% x 60 + y

y = $ 12 MN

So to make at least $40 million on her next film:

40 = 20% of x + 12

x = 140 MN

Answer 2

Salary relationships usually have behaviors that can be expressed through mathematical equations, for this case we must locate the information they give us, according to which the salary of the movie star
`S` is equal to a fixed basic remuneration
`b` plus a percentage
`x` of the gross income
`g`, that is:

`S = b + gx`

With this equation and the data they give us, we can solve the request so :

`\boldsymbol{1)} \; 32 = b + 100x\\\boldsymbol{2)} \; 24 = b + 60x`

We clear the basic remuneration
`b` from the second equation and replace in the first:

`\boldsymbol{2)} \; 24 = b + 60x\\24-60x = b\\\boldsymbol{1)} \; 32 = b + 100x\\32 = (24-60x) + 100x\\32-24=100x-60x\\8=40x\\(8)/(40) =x\\\boldsymbol{x=0,2}\\b=24-60x\\b=24-60(0,2)\\b=24-12\\\boldsymbol{b=12}`

Thus, with the fixed basic remuneration and the percentage of gross income calculated, we can estimate how much the following film should obtain so that the movie star obtains at least
`40` millions salary:

`40 = g (0.2) +12\\40-12 = g (0.2)\\(28)/(0.2y) = g\\\boldsymbol{g = 140}`

Answer

The minimum amount of gross income that the next film should generate is
`\$ 140` millions