Question

A movie theater has a seating capacity of 271. The theater charges $5.00 for children, $7.00 for students,

Answer 1

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 = $2x$

Ticket price for children = $\ 2x \times 5$

As per question statement, there were half as many adults as there are children,

so number of adult tickets = $x$

Ticket price for adults = $\ x \times 12$

Now, number of students =

$(271-x-2x)\\\Rightarrow (271-3x)$

Ticket price for students = $\ (271-3x) \times 7$

Total ticket sales = $1974

$\Rightarrow 12x+2x\times 5 +(271-3x)\times 7 = 1974\\\Rightarrow 22x-21x +(271 \times 7) = 1974\\\Rightarrow x = 1974 - 1897\\\Rightarrow x = 77$

So, number of adults attended = 77

number of children attended = 77 $\times$ 2 = 154

number of students attended = 271 - 77 - 154 = 40