Six hundred people attended the premiere of a motion picture. Adult tickets cost $12, and children were admitted for $9. If box office receipts totaled $6720, how many children attended the premiere?
Let's assume that the number of children who attended the premiere is "x".
The number of adults who attended the premiere can be calculated by subtracting the number of children from the total number of attendees. So, the number of adults is 600 - x.
The total revenue from the adult tickets can be calculated by multiplying the number of adult tickets (600 - x) by the cost of each adult ticket ($12). So, the revenue from the adult tickets is 12 * (600 - x).
Similarly, the total revenue from the children's tickets can be calculated by multiplying the number of children's tickets (x) by the cost of each children's ticket ($9). So, the revenue from the children's tickets is 9 * x.
Given that the total box office receipts were $6720, the equation can be written as:
12 * (600 - x) + 9 * x = 6720.
Now, let's solve the equation to find the value of x:
12 * 600 - 12 * x + 9 * x = 6720,
7200 - 12x + 9x = 6720,
-3x = 6720 - 7200,
-3x = -480,
x = -480 / -3,
x = 160.
Therefore, there were 160 children who attended the premiere of the motion picture.
To solve this problem, we can set up a system of equations based on the given information.
Let's assume that the number of adult attendees is A, and the number of children attendees is C.
From the problem, we know that:
1) The total number of attendees is 600: A + C = 600.
2) The box office receipts totaled $6720, which means the sum of the money from adult tickets and children tickets is $6720: 12A + 9C = 6720.
Now, we can solve this system of equations to find the values of A and C.
First, let's simplify equation 1 by isolating A:
A = 600 - C.
Now, substitute this value for A in equation 2:
12(600 - C) + 9C = 6720.
Simplify and solve for C:
7200 - 12C + 9C = 6720,
7200 - 3C = 6720,
-3C = -480,
C = (-480) / (-3),
C = 160.
So, there were 160 children who attended the premiere of the motion picture.