Respuesta :
Using a system of equations, it is found that:
- 126 children attended.
- 88 students attended.
- 63 adults attended.
What is a system of equations?
A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are:
- Variable x: Number of children that attended.
- Variable y: Number of students that attended.
- Variable z: Number of adults that attended.
The theater was full, hence:
x + y + z = 277.
There are half as many adults as there are children, hence:
x = 2z.
The theater charges $5.00 for children, $7.00 for students, and $12.00 for adults. The total ticket sales were of $2002, hence:
5x + 7y + 12z = 2002.
Replacing the second equation into the other two:
y + 3z = 277 -> y = 277 - 3z
7y + 22z = 2002.
Then:
7(277 - 3z) + 22z = 2002
z = 63
y = 277 - 3z = 277 - 3 x 63 = 88
x = 2z = 2 x 63 = 126.
Hence:
- 126 children attended.
- 88 students attended.
- 63 adults attended.
More can be learned about a system of equations at https://brainly.com/question/24342899
