Respuesta :
Let 'c' be the number of children, 'a' be the number of adults and 's' be the number of students in the theater.
Since, there are total 750 people in the theater.
So, c + s + a = 750 (Equation 1)
Now, it is given that there were half as many adults as children and students combined.
So, [tex]a= \frac{c+s}{2}[/tex]
So, [tex]c+s = 2a[/tex]
Putting the value of "c+s" in equation 1.
[tex]c+s+a=750[/tex]
[tex]2a+a = 750[/tex]
[tex]3a= 750[/tex]
a = 250
Now, it is given that the receipts totaled $4950 and it charges $5 for children, $7 for students, and $9 for adults.
So, [tex]( 5 \times c) +( 7 \times s )+ (9 \times a) = \$4950[/tex] (equation 2)
Since, [tex]c+s = 2a[/tex]
[tex]c+s = 500[/tex]
So, [tex]s = 500-c[/tex]
Substituting the values of 's' and 'a' in equation 2, we get
[tex]5c+7s+9a= 4950[/tex]
[tex]5c+ 7(500-c)+(9 \times 250) = 4950[/tex]
[tex]5c+3500-7c+2250=4950[/tex]
[tex]-2c= -800[/tex]
So, c = 400
Therefore, there were 400 children at the theater.
