As of January 2012, the top three grossing pictures worldwide were Avatar, Titanic and the finalenof Harry Potter series. Together they grossed $5.9 billion. Avatar earned just $300,000,000 less than both other movies combined, while Avatar and Titanic together were $600,000,000 less than four times Harry Potter. How much has each movie grossed?
in hundred millions
A + 3 = T + H
A + T + 6 = 4 H
A + T + H = 59
so
3 - T - 6 = T - 3 H
6 - H = 4 H -59
5 H = 65
H = 13
- T - 3 = T -3(13)
36 = 2 T
T = 18
A + 3 = 13 + 18
A = 28
so
A 2, 800, 000, 000
H 1, 300, 000, 000
T 1, 800, 000, 000
Avator--- a
Titanic --- t
Harry Potter -- p
let's just reduce all monies to millions
a+t+p = 5900 **
a = t+p-300 ---> a-t-p = -300 ***
a+t= 4p - 600 --- a+t-4p = -600 ****
add** and ***
2a = 5600
a = 2800
add *** and ****
2a - 5p = -900
5900 - 5p = -900
-5p = -6500
p = 1300
back in **
2800 + t + 1300 = 5900
t = 1800
a=2800, t=1800, p=1300
Switch back to millions
To find out how much each movie has grossed, let's assign variables to represent the gross earnings of each movie.
Let:
- A = Gross earnings of Avatar
- T = Gross earnings of Titanic
- H = Gross earnings of Harry Potter finale
From the given information:
1) Avatar earned $300,000,000 less than both Titanic and Harry Potter combined:
A = (T + H) - $300,000,000
2) Avatar and Titanic together were $600,000,000 less than four times the gross earnings of the Harry Potter finale:
A + T = (4 * H) - $600,000,000
We also know that the total gross earnings of Avatar, Titanic, and the Harry Potter finale combined equal $5.9 billion:
A + T + H = $5,900,000,000
Now, we have a system of three equations and three variables:
Equation 1: A = (T + H) - $300,000,000
Equation 2: A + T = (4 * H) - $600,000,000
Equation 3: A + T + H = $5,900,000,000
Solving this system of equations will give us the gross earnings of each movie.