Final answer:
To find the number of children, students, and adults who attended the movie theater, we can set up a system of equations based on the given information. By solving this system of equations, we can determine the values of C, S, and A.
Step-by-step explanation:
To find the number of children, students, and adults who attended the movie theater, we can set up a system of equations based on the given information. Let's assign variables:
C = number of children,
S = number of students,
A = number of adults.
From the problem statement, we know that there are half as many adults as there are children, so A = 0.5C. We also know that the total seating capacity is 303, so C + S + A = 303. In terms of ticket sales, we have $5.00C + $7.00S + $12.00A = $2200.
Substituting A = 0.5C into the second equation, we get $5.00C + $7.00S + $12.00(0.5C) = $2200. Simplifying this equation, we have $5.00C + $7.00S + $6.00C = $2200. Combining like terms, we get $11.00C + $7.00S = $2200.
From the first equation, we can solve for A in terms of C: A = 0.5C. Substituting this into the third equation, we get C + S + 0.5C = 303. Simplifying this equation, we have 1.5C + S = 303.
We now have a system of equations:
$11.00C + $7.00S = $2200,
1.5C + S = 303.
We can solve this system of equations by substitution or elimination to find the values of C, S, and A. Once we solve the equations, we can determine the number of children, students, and adults who attended the movie theater.