Respuesta :
Answer:
100 children
Step-by-step explanation:
Let x, y, and z denote the number of children, students, and adults, respectively.
A theater has a seating capacity of 750
So, [tex]x+y+z= 750[/tex] ---A
Theater charges $2 for children, $4 for students, and $6 for adults.
Cost for x children = 2x
Cost for y students = 4y
Cost for y adults = 6z
The receipts totaled $3300
So, [tex]2x+4y+6z=3300[/tex] ---B
Now we are given that there were half as many adults as children and students combined.
So,[tex]z=\frac{1}{2}(x+y)[/tex] ---C
[tex]2z=x+y[/tex]
Substitute the value of x+y in A
[tex]2z+z= 750[/tex]
[tex]3z= 750[/tex]
[tex]z= 250[/tex]
Substitute the value of z in A and B
In A
[tex]x+y+250= 750[/tex]
[tex]x+y=500[/tex] ---D
In B
[tex]2x+4y+6(250)=3300[/tex]
[tex]2x+4y=1800[/tex] ---E
Solve D and E
Substitute the value of x from D in E
[tex]2(500-y)+4y=1800[/tex]
[tex]1000-2y+4y=1800[/tex]
[tex]2y=800[/tex]
[tex]y=400[/tex]
Substitute the value of y in D
[tex]x+400=500[/tex]
x=100
Hence 100 children attended the show
