Answer :
Answer:
Children attended = 154
Students attended = 40
Adults attended = 77
Step-by-step explanation:
Seating capacity = 271
Charges for each children ticket = $5
Charges for each student ticket = $7
Charges for each adult ticket = $12
Let number of children tickets = [tex]2x[/tex]
Ticket price for children = [tex]\$ 2x \times 5[/tex]
As per question statement, there were half as many adults as there are children,
so number of adult tickets = [tex]x[/tex]
Ticket price for adults = [tex]\$ x \times 12[/tex]
Now, number of students =
[tex](271-x-2x)\\\Rightarrow (271-3x)[/tex]
Ticket price for students = [tex]\$ (271-3x) \times 7[/tex]
Total ticket sales = $1974
[tex]\Rightarrow 12x+2x\times 5 +(271-3x)\times 7 = 1974\\\Rightarrow 22x-21x +(271 \times 7) = 1974\\\Rightarrow x = 1974 - 1897\\\Rightarrow x = 77[/tex]
So, number of adults attended = 77
number of children attended = 77 [tex]\times[/tex] 2 = 154
number of students attended = 271 - 77 - 154 = 40